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作者： imtoken钱包下载包

2024-03-13 06:04:43

What is Hexadecimal Numbers System? Table, Conversions, Examples

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MathsMath ArticleHexadecimal Number System

Hexadecimal Number System

The hexadecimal number system is a type of number system, that has a base value equal to 16. It is also pronounced sometimes as ‘hex’. Hexadecimal numbers are represented by only 16 symbols. These symbols or values are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F. Each digit represents a decimal value. For example, D is equal to base-10 13.

Hexadecimal number systems can be converted to other number systems such as binary number (base-2), octal number (base-8) and decimal number systems (base-10). The concept of the number system is widely explained in the syllabus of Class 9.

The list of 16 hexadecimal digits with their equivalent decimal, octal and binary representation is given here in the form of a table, which will help in number system conversion. This list can be used as a translator or converter also.

Hexadecimal Number System Table

Below is the table of hexadecimal number systems with equivalent values of the binary and decimal number systems.

Decimal Numbers

4-bit Binary Number

Hexadecimal Number

0000

0001

0010

0011

0100

0101

0110

0111

1000

1001

1010

1011

1100

1101

1110

1111

Below is the link to download the table. Students can download the PDF and learn offline too.

Download PDF – Hexadecimal Number System

Hexadecimal Number System Conversions

As we know, there are 16 digits in the hexadecimal number system, represented from 0 to 9 same as decimals, but after that, it starts with an alphabetical representation of preceding numbers such as A, B, C, D and E. Let us see the conversion of ‘hex’ into other number systems.

Hexadecimal to Decimal Conversion

Here, you will see the representation of a hexadecimal number into decimal form.

Hexadecimal

Decimal

Decimal to Hexadecimal Conversion

You have learned how to convert hexadecimal numbers to decimal numbers. Now let us find out how we can convert a decimal number into a hexadecimal number system. Follow the below steps:

Firstly divide the number by 16

Take the quotient and divide again by 16

The remainder left will produce the hex value

Repeats the steps until the quotient has become 0

Example: Convert (242)10 into hexadecimal.

Solution: Divide 242 by 16 and repeat the steps, till the quotient is left as 0.

Therefore, (242)10 = (F2)16

Hexadecimal to Octal Conversion

Here, you will see the representation of a hexadecimal number into octal number form.

Hexadecimal

Octal

Octal to Hexadecimal Conversion

To convert octal to hex, we have to first convert octal number to decimal and then decimal to hexadecimal. Let us understand it with the help of an example;

Example: Convert (121)8 into hexadecimal.

Solution: First convert 121 into decimal number.

⇒ 1 × 82 + 2 × 81 + 1 × 80

⇒ 1 × 64 + 2 × 8 + 1 × 1

⇒ 64 + 16 + 1

⇒ 81

(121)8 = 8110

Now converting 8110 into a hexadecimal number.

Therefore, 8110 = 5116

Hexadecimal to Binary Conversion

Here, you will see the representation of a hexadecimal number into binary form. We can use only 4 digits to represent each hexadecimal number, where each group has a distinct value from 0000 (for 0) and 1111 (for F= 15 =8 + 4 + 2 + 1).

Hexadecimal

Binary

100

101

110

111

1000

1001

1010

1011

1100

1101

1110

1111

Binary to Hexadecimal Conversion

Binary to hexadecimal conversion is a simple method to do. You just have to put the values of the binary number to the relevant hexadecimal number.

Example: Convert (11100011)2 to hexadecimal.

Solution: From the table, we can write, 11100011 as E3.

Therefore, (11100011)2 = (E3)16

Facts of Hexadecimal Number System

Out of many types of number representation techniques, the Hexadecimal number system is one having a value of base 16.

So Hexadecimal numbers have 16 symbols or digital values, i.e 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.

A, B, C, D, E, F are single bit representations of 10, 11, 12, 13, 14 and 15 respectively.

The addition of either an o prefix or an h prefix indicates Hexadecimal.

A power of 16 is the weight of the position of every digit.

Solved Examples on Hexadecimal number system

Example 1: What is 5C6 (Hexadecimal)?

Solution: Step 1: The “5 “ is the “16 x 16” position, so that means 5 x16 x16

Step 2: The ‘C’ (12) is in the “16” position, so that means 12 x 16.

Step 3: The “6” in the “1” position so that means 6.

Answer is : 5C6 = 5 x 16 x 16 + 12 x 16 +6 = (1478 ) in Decimal.

Example 2: What is 3C5 (Hexadecimal)?

Solution: Step 1: The “3 “ is the “16 x 16” position, so that means 3 x16 x16

Step 2: The ‘C’ (12) is in the “16” position, so that means 12 x 16.

Step 3: The “5” is in the “1” position so that means 5.

Answer is : 3C5 = 3 x 16 x 16 + 12 x 16 + 5 = (965) in Decimal.

Example 3: What is 7B5 (Hexadecimal)?

Solution: Step 1: The “7 “ is the “16 x 16” position, so that means 7 x16 x16

Step 2: The ‘B’ (11) is in the “11” position, so that means 11 x 16.

Step 3: The 5” in the “1” position so that means 5.

Answer is : 7B5 = 7 x 16 x 16 + 11 x 16 +5 = (1973) in Decimal.

Example 4: What is 2E8 (Hexadecimal)?

Solution: Step 1: The “2 “ is the “16 x 16” position, so that means 2 x16 x16

Step 2: The ‘E’ (14) is in the “16” position, so that means 14 x 16.

Step 3: The “2” is in the “1” position so that means 2.

Answer is : 2E8 = 2 x 16 x 16 + 14 x 16 +8 = (744) in Decimal.

Example 5: What is 4F8 (Hexadecimal)?

Solution: Step 1: The “4 “ is the “16 x 16” position, so that means 4 x16 x16

Step 2: The ‘F’ (15) is in the “16” position, so that means 15 x 16.

Step 3: The “8” is in the “1” position, which means 8.

Answer is : 4F8 = 4 x16 x 16 + 15 x 16 +8 = (1272) in Decimal.

Practice Questions

What is 5D16 in decimal number?

Convert decimal number 21 into a hexadecimal number.

What is 01101112 in hexadecimal?

Number System Conversion

Binary Number System

Octal Number System

Hexadecimal Calculator

Number System For Class

Important Questions Class 9 Maths Chapter 1 Number System

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Frequently Asked Questions – FAQsQ1 What is a hexadecimal number system?The hexadecimal number system is a number system with base-16. It is represented by only 16 digits or values.Q2 What are the 16 digits of the hexadecimal number system?The 16 digits of the hexadecimal number system are 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.Q3 What is the use of the hexadecimal number system?Hexadecimal number systems are used for computer programming and designing. Since the computer understands only binary digits (0 and 1), thus each hexadecimal digit represents four binary digits.Q4 What is 3CD (hexadecimal)?3CD is a hexadecimal number that is equivalent to decimal number 973.

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What is a Hexagon? Definition, Properties, Area, Perimeter, Facts

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Hexagon – Definition, Types, Properties, Examples, FAQs

Home » Math Vocabluary » Hexagon – Definition, Types, Properties, Examples, FAQs

What is a Hexagon? Types of HexagonsClassification of hexagons based on their anglesSolved Examples on HexagonPractice Problems On HexagonFrequently Asked Questions On Hexagon

What is a Hexagon?

In geometry, a hexagon can be defined as a closed two-dimensional polygon with six sides.

Hexagon has 6 vertices and 6 angles also.

Hexa means six and gonia means angles.

Examples

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Hexagon in Real Life

We can find the shape of a hexagon in a honeycomb, a football, face of pencil, and floor tiles.

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Types of Hexagons

Hexagonal shape is classified into several types based on the measure of sides and angles.

Classification of hexagons based on their sides

1. Regular Hexagon

When the length of all the sides and measure of all the angles are equal, it is a regular hexagon. All interior angles of a regular hexagon are 120 degrees each.

Properties of a Regular Hexagon

All the sides are equal in length.

All the interior angles measure 120°.

All the exterior angles measure 60°.

Since all angles are equal in a regular hexagon, each angle is 120o and the sum of all the interior angles is 720o.

A regular hexagon can be divided into six equilateral triangles.

The opposite sides of a regular hexagon are parallel to each other.

A regular hexagon is also a convex hexagon.

Symmetry in regular hexagon:

A regular hexagon has 6 lines of symmetry and a rotational symmetry of order 6

6 lines of symmetrySix 60° angles of rotation

2. Irregular Hexagon

In an irregular hexagon, the length of sides and measure of angles do not have the same measure.

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Classification of hexagons based on their angles

1. Convex Hexagon

For convex hexagons, all of its interior angles must be less than 180 degrees, and all the vertices are pointed outwards. Convex hexagons can be regular or irregular.

2. Concave Hexagon

For concave hexagons, at least one of its interior angles must be greater than 180° and at least one of its vertex points inwards.

Properties of Hexagon

It is two-dimensional.

It has six sides, six edges and six vertices.

The sum of the interior angles is 720 degrees.

It has nine diagonals.

Perimeter of a Hexagon

The perimeter of a hexagon is the sum of the length of all 6 sides.

Perimeter = AB + BC + CD + DE + EF + FA

In regular hexagons, all sides are equal in length. So, the perimeter of a regular hexagon is six times the length of one side.

Perimeter = a + a + a + a + a + a = 6a

Solved Examples on Hexagon

Example 1: Find the perimeter of a regular hexagon having each side measure 20 cm.

Solution:

Perimeter of regular hexagon = 6 × length of side

= 6 × 20 cm

= 120 cm

So, the perimeter of the hexagon is 120 cm.

Example 2: The perimeter of a regular hexagon is 36 cm. What is the length of its sides?

Solution:

Perimeter of regular hexagon = 6 × length of side

36 = 6 × length of side

Length of side = 366 cm = 6 cm

So, the length of its sides is 6 cm.

Example 3: Five angles of a hexagon measure 110° each. What is the measure of the sixth angle?

Solution:

Sum of the interior angles in hexagon = 720°

Sum of five angles = 5 × 110° = 550°

Sixth angle = 720° – 550° = 170°

So, the measure of the sixth angle is 170°.

Practice Problems On Hexagon

HexagonAttend this Quiz & Test your knowledge.1What is the measure of each interior angle of a regular hexagon?60°100°120°720°CorrectIncorrectCorrect answer is: 120°The sum of the interior angles of a hexagon is 720° For a regular hexagon all the sides are of the same length and all interior angles are equal. So, each interior angle= 720/6 = 120° So, the measure of the interior angle of a regular hexagon is 120°.2A plane with six sides is classified aspentagonhexagonheptagonoctagonCorrectIncorrectCorrect answer is: hexagonHexagon is a two dimensional polygon with six sides.3The hexagon is said to be convex hexagon if none of its interior angles is 90°less than 90°more than 90° and less than 180°more than 180°CorrectIncorrectCorrect answer is: more than 180°more than 180° For convex hexagons, all of its interior angles must be less than 180 degrees. For concave hexagons, at least one of its interior angles must be greater than 180°.4A regular hexagon has how many lines of symmetry 4689CorrectIncorrectCorrect answer is: 6A regular hexagon has 6 lines of symmetry. In a regular polygon the lines of symmetry are equal to the number of sides. So there will be 6 lines of symmetry for a regular hexagon.

Frequently Asked Questions On Hexagon

How many types of hexagons are there?

There are four types of hexagons. These are regular hexagons, irregular hexagons, concave hexagons, and concave hexagons.

What are the three characteristics of a hexagon?

Hexagon has 6 sides, 6 angles and 6 vertices.

What is the sum of all interior angles of a hexagon?

The sum of all interior angles of a hexagon is 720°.

How many diagonals does a hexagon have?

A hexagon has 9 diagonals.

Does a hexagon always have equal sides?

No, hexagons can have sides with different lengths. Regular hexagon has all sides are equal in length.

Are all six-sided shapes hexagon?

Yes, all six sided shapes are called hexagons.

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HEXA - Wikipedia

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1Function

2Gene mutations resulting in Tay–Sachs disease

3Gene therapies for Tay-Sachs

4References

5Further reading

6External links

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HEXA

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From Wikipedia, the free encyclopedia

Protein-coding gene in the species Homo sapiens

HEXAAvailable structuresPDBOrtholog search: PDBe RCSB List of PDB id codes2GJX, 2GK1IdentifiersAliasesHEXA, TSD, hexosaminidase subunit alphaExternal IDsOMIM: 606869 MGI: 96073 HomoloGene: 20146 GeneCards: HEXA Gene location (Human)Chr.Chromosome 15 (human)[1]Band15q23Start72,340,924 bp[1]End72,376,420 bp[1]Gene location (Mouse)Chr.Chromosome 9 (mouse)[2]Band9 B|9 32.02 cMStart59,446,823 bp[2]End59,472,392 bp[2]RNA expression patternBgeeHumanMouse (ortholog)Top expressed ingallbladderstromal cell of endometriumleft lobe of thyroid glandright coronary arteryright lobe of thyroid glandleft adrenal glandright uterine tuberight lungrectumupper lobe of left lungTop expressed incalvariabody of femuririsaortic valvecrypt of lieberkuhn of small intestineascending aortaciliary bodyislet of LangerhansPaneth cellutricleMore reference expression dataBioGPSn/aGene ontologyMolecular function

acetylglucosaminyltransferase activity

protein heterodimerization activity

hydrolase activity, hydrolyzing O-glycosyl compounds

hydrolase activity

hydrolase activity, acting on glycosyl bonds

beta-N-acetylhexosaminidase activity

N-acetyl-beta-D-galactosaminidase activity

protein binding

Cellular component

extracellular exosome

membrane

lysosome

lysosomal lumen

azurophil granule

Biological process

hyaluronan catabolic process

glycosaminoglycan biosynthetic process

metabolism

glycosphingolipid metabolic process

chondroitin sulfate catabolic process

keratan sulfate catabolic process

carbohydrate metabolic process

Sources:Amigo / QuickGOOrthologsSpeciesHumanMouseEntrez307315211EnsemblENSG00000213614ENSMUSG00000025232UniProtP06865P29416RefSeq (mRNA)NM_000520NM_001318825NM_010421RefSeq (protein)NP_000511NP_001305754NP_034551Location (UCSC)Chr 15: 72.34 – 72.38 MbChr 9: 59.45 – 59.47 MbPubMed search[3][4]WikidataView/Edit HumanView/Edit Mouse

HEXA gene is located on the long (q) arm of chromosome 15 at position 24.1.

Hexosaminidase A (alpha polypeptide), also known as HEXA, is an enzyme that in humans is encoded by the HEXA gene, located on the 15th chromosome.[5][6]

Hexosaminidase A and the cofactor GM2 activator protein catalyze the degradation of the GM2 gangliosides and other molecules containing terminal N-acetyl hexosamines.[7] Hexosaminidase A is a heterodimer composed of an alpha subunit (this protein) and a beta subunit. The alpha subunit polypeptide is encoded by the HEXA gene while the beta subunit is encoded by the HEXB gene. Gene mutations in the gene encoding the beta subunit (HEXB) often result in Sandhoff disease; whereas, mutations in the gene encoding the alpha subunit (HEXA, this gene) decrease the hydrolysis of GM2 gangliosides, which is the main cause of Tay–Sachs disease.[8]

Function[edit]

Even though the alpha and beta subunits of hexosaminidase A can both cleave GalNAc residues, only the alpha subunit is able to hydrolyze GM2 gangliosides. The alpha subunit contains a key residue, Arg-424, which is essential for binding the N-acetyl-neuraminic residue of GM2 gangliosides. The alpha subunit can hydrolyze GM2 gangliosides because it contains a loop structure consisting of the amino acids: Gly-280, Ser-281, Glu-282, and Pro-283. The loop is absent in the beta subunit, but it serves as an ideal structure for the binding of the GM2 activator protein (GM2AP) in the alpha subunit. A combination of Arg-424 and the amino acids that cause the formation of the loop allow the alpha subunit to hydrolyze GM2 gangliosides into GM3 gangliosides by removing the N-acetylgalactosamine (GalNAc) residue from GM2 gangliosides.[9]

Gene mutations resulting in Tay–Sachs disease[edit]

There are numerous mutations that lead to hexosaminidase A deficiency including gene deletions, nonsense mutations, and missense mutations. Tay–Sachs disease occurs when hexosaminidase A loses its ability to function. People with Tay–Sachs disease are unable to remove the GalNAc residue from the GM2 ganglioside, and as a result, they end up storing 100 to 1000 times more GM2 gangliosides in the brain than the normal person. Over 100 different mutations have been discovered just in infantile cases of Tay–Sachs disease alone.[10]

The most common mutation, which occurs in over 80 percent of Tay–Sachs patients, results from a four base pair addition (TATC) in exon 11 of the Hex A gene. This insertion leads to an early stop codon, which causes the Hex A deficiency.[11]

Children born with Tay–Sachs usually die between two and six years of age from aspiration and pneumonia. Tay–Sachs causes cerebral degeneration and blindness. Patients also experience flaccid extremities and seizures. There is no cure for Tay–Sachs disease.[10]

Gene therapies for Tay-Sachs[edit]

The HEXA gene is a protein encoding gene that codes for the lysosomal enzyme beta-hexosaminidase. This enzyme, combined with the GM2 activator protein, is responsible for the breakdown of ganglioside GM2 within the lysosome. Defects in the HEXA gene, however, prevent this degradation, leading to a buildup of toxins in brain and spinal cord cells. This fatal genetic disorder is called Tay-Sachs disease. Because the Tay-Sachs gene defect mainly affects neural cells, a patient with the HEXA mutation will experience a quick deterioration of motor and mental function before dying around the age of three or four.[citation needed]

A “knockout” model, which is a mouse that has been genetically modified to observe the effects of inactivation of or damage to certain genes, found that the mice that were administered the HEXA gene experienced many of the same symptoms of Tay-Sachs, with one exception: GM2 buildup was distributed differently in the brains of the mice than in those of a typical human Tay-Sachs patient.[citation needed] This model has allowed scientists to research gene therapies for HEXA defects. One study, done on mice, successfully reestablished beta-hexoaminidase levels and removed the toxic cell buildup by using a non-replicated Herpes simplex vector to code for the missing gene.[citation needed]

References[edit]

^ a b c GRCh38: Ensembl release 89: ENSG00000213614 - Ensembl, May 2017

^ a b c GRCm38: Ensembl release 89: ENSMUSG00000025232 - Ensembl, May 2017

^ "Human PubMed Reference:". National Center for Biotechnology Information, U.S. National Library of Medicine.

^ "Mouse PubMed Reference:". National Center for Biotechnology Information, U.S. National Library of Medicine.

^ Korneluk RG, Mahuran DJ, Neote K, Klavins MH, O'Dowd BF, Tropak M, Willard HF, Anderson MJ, Lowden JA, Gravel RA (June 1986). "Isolation of cDNA clones coding for the alpha-subunit of human beta-hexosaminidase. Extensive homology between the alpha- and beta-subunits and studies on Tay-Sachs disease". The Journal of Biological Chemistry. 261 (18): 8407–13. doi:10.1016/S0021-9258(19)83927-3. PMID 3013851.

^ Proia RL, Soravia E (April 1987). "Organization of the gene encoding the human beta-hexosaminidase alpha-chain". The Journal of Biological Chemistry. 262 (12): 5677–81. doi:10.1016/S0021-9258(18)45628-1. PMID 2952641.

^ Knapp S, Vocadlo D, Gao Z, Kirk B, Lou J, Withers SG (1996). "NAG-thiazoline, an N-acetylbeta-hexosaminidase inhibitor that implicates acetamido participation". J. Am. Chem. Soc. 118 (28): 6804–6805. doi:10.1021/ja960826u.

^ Mark BL, Mahuran DJ, Cherney MM, Zhao D, Knapp S, James MN (April 2003). "Crystal structure of human beta-hexosaminidase B: understanding the molecular basis of Sandhoff and Tay-Sachs disease". Journal of Molecular Biology. 327 (5): 1093–109. doi:10.1016/S0022-2836(03)00216-X. PMC 2910754. PMID 12662933.

^ Lemieux MJ, Mark BL, Cherney MM, Withers SG, Mahuran DJ, James MN (June 2006). "Crystallographic structure of human beta-hexosaminidase A: interpretation of Tay-Sachs mutations and loss of GM2 ganglioside hydrolysis". Journal of Molecular Biology. 359 (4): 913–29. doi:10.1016/j.jmb.2006.04.004. PMC 2910082. PMID 16698036.

^ a b Ozand PT, Nyhan WL, Barshop BA (2005). "Part Thirteen Lipid Storage Disorders: Tay-Sachs disease/hexosaminidase A deficiency". Atlas of metabolic diseases. London: Hodder Arnold. pp. 539–546. ISBN 0-340-80970-1.

^ Boles DJ, Proia RL (March 1995). "The molecular basis of HEXA mRNA deficiency caused by the most common Tay-Sachs disease mutation". American Journal of Human Genetics. 56 (3): 716–24. PMC 1801160. PMID 7887427.

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A regular decimal number is the sum of the digits multiplied with power of 10.

137 in base 10 is equal to each digit multiplied with its corresponding power of 10:

13710 = 1×102+3×101+7×100 = 100+30+7

Hex numbers are read the same way, but each digit counts power of 16 instead of power of 10.

For hex number with n digits:

dn-1 ... d3 d2 d1 d0

Multiply each digit of the hex number with its corresponding power of 16 and sum:

decimal = dn-1×16n-1 + ... + d3×163 + d2×162 + d1×161+d0×160

Example #1

3B in base 16 is equal to each digit multiplied with its corresponding 16n:

3B16 = 3×161+11×160 = 48+11 = 5910

Example #2

E7A9 in base 16 is equal to each digit multiplied with its corresponding 16n:

E7A916 = 14×163+7×162+10×161+9×160 = 57344+1792+160+9 = 5930510

Example #3

0.8 in base 16:

0.816 = 0×160+8×16-1

= 0+0.5 = 0.510

Hex to decimal conversion table

Hexbase 16

Decimalbase 10

Calculation

1×161+0×160 = 16

1×161+1×160 = 17

1×161+2×160 = 18

1×161+3×160 = 19

1×161+4×160 = 20

1×161+5×160 = 21

1×161+6×160 = 22

1×161+7×160 = 23

1×161+8×160 = 24

1×161+9×160 = 25

1×161+10×160 = 26

1×161+11×160 = 27

1×161+12×160 = 28

1×161+13×160 = 29

1×161+14×160 = 30

1×161+15×160 = 31

2×161+0×160 = 32

3×161+0×160 = 48

4×161+0×160 = 64

5×161+0×160 = 80

6×161+0×160 = 96

112

7×161+0×160 = 112

128

8×161+0×160 = 128

144

9×161+0×160 = 144

160

10×161+0×160 = 160

176

11×161+0×160 = 176

192

12×161+0×160 = 192

208

13×161+0×160 = 208

224

14×161+0×160 = 224

240

15×161+0×160 = 240

100

256

1×162+0×161+0×160 = 256

200

512

2×162+0×161+0×160

= 512

300

768

3×162+0×161+0×160

= 768

400

1024

4×162+0×161+0×160

= 1024

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HTML Color Codes

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HEX

#FF5733

RGB

255, 87, 51

HSL

11, 80%, 60%

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IndianRed

#CD5C5C

rgb(205, 92, 92)

LightCoral

#F08080

rgb(240, 128, 128)

Salmon

#FA8072

rgb(250, 128, 114)

DarkSalmon

#E9967A

rgb(233, 150, 122)

LightSalmon

#FFA07A

rgb(255, 160, 122)

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#DFFF00

223, 255, 0

#FFBF00

255, 191, 0

#FF7F50

255, 127, 80

#DE3163

222, 49, 99

#9FE2BF

159, 226, 191

#40E0D0

64, 224, 208

#6495ED

100, 149, 237

#CCCCFF

204, 204, 255

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Hex color codes

The most popular are Hex color codes; three byte hexadecimal numbers (meaning they consist of six digits), with each byte, or pair of characters in the Hex code, representing the intensity of red, green and blue in the color respectively.

#XXXXXX

Hex code byte values range from 00, which is the lowest intensity of a color, to FF which represents the highest intensity. The color white, for example, is made by mixing each of the three primary colors at their full intensity, resulting in the Hex color code of #FFFFFF.

#FFFFFF

Black, the absence of any color on a screen display, is the complete opposite, with each color displayed at their lowest possible intensity and a Hex color code of #000000.

#000000

Understanding the basics of Hex color code notation we can create grayscale colors very easily, since they consist of equal intensities of each color:

#454545

#999999

The three primary colors, red, green and blue, are made by mixing the highest intensity of the desired color with the lowest intensities of the other two:

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#0000FF

With modern browsers supporting the full spectrum of 24-bit color, there are 16,777,216 different color possibilities. Use our color picker to explore all 16.7 million of them, or if that’s too many, check out our color charts for a selection of palettes focused on flat design, Material design and web safe colors.

List of common HTML color codes

Color

Name

Hex Code

RGB Code

White

#FFFFFF

rgb(255, 255, 255)

Silver

#C0C0C0

rgb(192, 192, 192)

Gray

#808080

rgb(128, 128, 128)

Black

#000000

rgb(0, 0, 0)

Red

#FF0000

rgb(255, 0, 0)

Maroon

#800000

rgb(128, 0, 0)

Yellow

#FFFF00

rgb(255, 255, 0)

Olive

#808000

rgb(128, 128, 0)

Lime

#00FF00

rgb(0, 255, 0)

Green

#008000

rgb(0, 128, 0)

Aqua

#00FFFF

rgb(0, 255, 255)

Teal

#008080

rgb(0, 128, 128)

Blue

#0000FF

rgb(0, 0, 255)

Navy

#000080

rgb(0, 0, 128)

Fuchsia

#FF00FF

rgb(255, 0, 255)

Purple

#800080

rgb(128, 0, 128)

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HEXA（ヘキサ） - ヘキサ（HEXA）NFTマーケットプレイス

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HEXA NFTとは

NFT徹底解説

インタビュー

NFTを探す

NFTを販売

仮想通貨・ウォレット不要NFTマーケット

最大級のマーケットC2C型NFTマーケットプレイスとして日本最大級

日本円完結仮想通貨は一切不要すべて日本円で完結

コミュニティNFT保有者限定で入れるコミュニティ機能

HEXAメタバース購入したNFTを飾って楽しめる

HEXA NFTマーケットへABOUT HEXAHEXAについて日本円だけでNFTの発行や売買ができる日本初のNFTマーケットプレイスです。クレジットカード決済でPCスマホから簡単にNFTを購入できます。仮想通貨やウォレットは一切不要で、すぐにNFTを購入したり、売却したり、発行できます。HEXAメタバースと連動し、NFTはHEXA LANDや住民票NFTがあれば自分のメタバース部屋に飾ることもできます。また、WEB3.0型オンラインサロンやファンクラブなどのコミュニティ機能も搭載しています。

デジタル資産NFTとはNFTはNon-Fungible Token（代替不可能なトークン）の略称であり、デジタルデータの所有権をブロックチェーン上に記録することで、これまではコピーして無数に複製ができたデジタルデータを1つだけに特定し、移転・売買できるようにしたものです。美術品などと同様に新たな資産として注目されています。NFTについて詳しくはこちら。NFT化でデジタルデータに価値を持たせる「HEXA（ヘキサ）」では、画像・動画・音声・3Dデータや記事をNFT化することによって、デジタルデータを1点物に変えて価値を創り出します。現実世界での美術品やサイン色紙などの1点物のやり取りのように、ツイートやデジタル作品のNFTもやり取りできるようになります。イーサリアム及びポリゴン（MATIC）のパブリックチェーンを使ったグローバルなNFTが発行できます。

無形の価値をファンと共有できるファンと一緒に盛り上がった瞬間や記念すべきシーン、思い入れのアート作品など、今まで価値の表現が難しかった唯一無二のオリジナルをNFTとしてブロックチェーンに刻み、ファンとその価値を共有することができます。

新しいファンの獲得にもつながるNFTの発行をきっかけに発行者を知り、また購入して応援してくれる新しいファンの獲得につながる可能性があります。NFTは将来の値上がりする可能性もあり、将来に期待して購入し、強くサポートしてくれるファンの獲得につながります。

時間・金銭的負荷ゼロで収益獲得発行に費用はかかりません。既に所有されているあらゆるデータ（写真・動画・音声・記事など）を簡単３ステップでNFT化するだけです。SNSアカウントさえあれば誰でもすぐに発行可能です。在庫リスクも持ち出し費用も一切なく、収益を得られます。STEP簡単ステップで画像・動画・音声・3Dデータや記事をNFT化01

アカウントをワンクリックで認証02

NFT化したい作品・ツイートを選択03

条件を決めて発行MERITなぜHEXAで発行するのか？

日本円完結日本円での販売が可能で、購入者も日本円で転売できます。そのため、仮想通貨なしで日本円でNFTの売買ができ、購入者層の幅が広がります。

ロイヤリティHEXAで転売されても継続して著作者に収益が入り続けます。将来値段が高騰した場合も恩恵を受けることができます。

メタバース空間HEXA独自のメタバース空間に保有するNFTを飾って楽しんだり友人を招待することができ、保有や転売をするだけではない楽しみ方があります。

袋とじNFTNFT保有者だけが見れる、メッセージや画像を入れた袋とじ・トレカ型のNFTを発行することができます。

コミュニティ機能NFT保有者限定のWEB3.0型コミュニティ機能を使うことで、オンラインサロンやファンクラブなど様々な活用ができます。

仮想通貨・ガス代不要HEXA（ヘキサ）ではNFTの販売のために仮想通貨やウォレット、ガス代は不要です。また、販売収益も円で受け取りが可能ですので、仮想通貨による取引がないため、複雑な仮想通貨の会計処理も不要です。

HEXAメタバースの部屋事例

ハルコメパイNFT【okometo-オコメト-】@pai3art

天々堂 TENTEN-DOU NFT@TENTENDOU_NFT

DaiSukE ZaImA@3DZ_WorlD

こはくの天使@KohakuNoTenshi

SABOTENSHI-NFTさぼ天使@ISIKOROCRYPTO

reima planet©︎@Backto_planet

ハルノキ⬣第五回HEXA公認アンバサダー@harunokikobo

SABOTENSHI-NFTさぼ天使@ISIKOROCRYPTO

と～こ NFT地球を守り隊✒️@tokotokotoko31

PARTNERパートナー東京証券取引所に上場する企業グループとの業務提携や資本提携を行っている信頼と安心のHEXA（ヘキサ）

Government Partner官公庁との包括連携山形県西川町とNFT関連分野で包括連携協定を締結しているHEXA（ヘキサ）

MARKET CONNECTマーケット連携TVアニメに特化したテレビ東京メディアネットのNFTマーケット「fancity」とのマーケット連携を行っているHEXA（ヘキサ）

ARCHIVEMENTS発行実績

もっと見るMEDIAメディア掲載実績

画像・動画・音声・記事等をファンと共有既に所有しているデータをNFT化するだけで始められます。

NFTを発行する

お問い合わせFAQよくある質問NFT発行や購入の詳細マニュアルが欲しい発行者向けのマニュアルはこちらからご確認ください。購入者向けのマニュアルはこちらからご確認ください。購入決済に使用できるクレジットカードを教えてほしいVISA、Master、JCB、American Expressがご利用いただけます。ただし、3Dセキュア認証の設定が必要です。海外で発行されたクレジットカードでもご決済が可能です。デビット・プリペイドカードもご利用可能ですが、同じタイミングで複数の方が同じNFTを購入されようとされるなど与信確認後にエラーが生じた場合、一時的に残高が引き落とされて返金される処理がカード会社様で発生いたします。また、デビット・プリペイドの返金については翌営業日～数日となり、デビット・プリペイドカード会社様の銀行処理（デビット・プリペイドの運営銀行）によって各社異なり、タイミングについてはカード会社様にお問い合わせいただく形となりますのでご注意ください。NFT発行までの詳細な流れとマニュアルが欲しい発行者向けのマニュアルはこちらからご確認くださいHEXAにログインするツイッターアカウントを変更したいHEXAをご利用されているウェブブラウザで、ツイッターサイトに戻り、ツイッター上でアカウント切り替えを行います。その後、HEXAに戻ってログアウト・ログインを行うと、ツイッターログイン中のアカウントで認証・ログインが可能となります。よくあるケースですが、メールからリンクをクリックされますと、通常お使いのブラウザではなく、メールアプリ内ブラウザが開かれます。そのメールアプリ内ブラウザで別のツイッターアカウントでログインされているケースがございます。この場合、該当のリンクをクリックして既にHEXAにログインいただいている別のブラウザでお試しいただくか、メールアプリ内ブラウザでツイッターを開き、アカウントを切り替えてHEXAに再ログインをいただけますと幸いです。HEXAでだけクレジットカード決済が通らないNFTの決済には3Dセキュア2.0の高度な認証が求められております。ご利用いただいているカード会社様に確認される際、カード会社として制限がかかっていない、ご利用サービス側にお問い合わせくださいと返答があった場合でも、クレジットカード会社のカスタマーサポート担当の方が3Dセキュア2.0について把握されていないケースが多く確認されております。その場合、「NFTの決済で3Dセキュア2.0（EMV 3Dセキュア）なのですが、2段階目の認証も解除されていますか？」とご確認頂くことで解消される場合が多数報告されておりますのでご確認ください。NFT化の審査が通らない他者投稿の引用リツイート・ツイートが含まれる場合は承認されないケースが多くなっています。また、他者の著作物や商標を含むものについても著作権を100%発行者様で取得している可能性が低いと考えられるものはNGとなります。100%ご自身で権利を保有されていてもNGとなる場合は、ツイッターアカウントやNFTにその旨を示す情報を入れていただくことで審査がOKとなるケースもございます。よくあるNG事例などはこちら。発行申請した動画が再生されない、NGになるサムネイル設定画面で動画が再生されることを確認の上、ご申請いただけますと幸いです。再生されない場合、MP4動画のformatをAVC方式にして出力いただけますと幸いです。プレビューで再生されない動画を申請頂いた場合は、審査時にNGとなります発行申請して発売したNFTが売れなかった場合の費用は？一切費用が発生することはありません。HEXA（ヘキサ）ではNFTの発行申請を頂き販売された場合、販売期間内（自由に設定いただけます）に売れなかった場合、料金が発生することはありません。そのため、NFT発行に伴って費用をご請求することはございませんのでご安心ください。売れた場合は、その販売金額から所定（発行申請時にご確認いただけます）の調達手数料が差し引かれます。HEXA内での日本円での転売と仮想通貨での転売販売されたHEXA NFTはHEXA内で日本円や仮想通貨で転売することが可能です。NFT保有者限定コンテンツとは何ですか？NFTを保有している人だけが見れるメッセージおよびコンテンツを設定することができます。NFTを購入してくれた方だけに伝えたいメッセージや見せたいコンテンツを設定できます。ロイヤリティとは何ですか？発行時点で二次流通時のロイヤリティのパーセンテージを設定することで、HEXA内で日本円でNFTが転売された場合は発行者に転売金額×ロイヤリティが継続的に支払われます。これによってNFT販売時に安く販売しすぎてしまった場合も、転売マーケットで高値が付けば、著作者は継続的に恩恵を受けることができます。また、転売者も転売によって著作者をサポートすることができます。報酬の受け取り方法とタイミングについて教えてください日本円での販売の場合、販売されたNFTの販売代金から発行時に設定された調達手数料を差し引いた金額を銀行振り込みによりお振込みさせて頂きます（銀行振込手数料は弊社負担です）。販売後、お振込口座情報をご入力いただき、月末締め・翌月末払いにてお支払いさせていただきます。ナイスを押して再読込すると押されてないときがあるアクセス対策のためサイト表示の情報更新に数十秒から最大約1分の時間差があります。ナイスを押してすぐページ再読込すると、ナイスが押されていない見た目になることがありますが、記録されており、数十秒後に再読込で更新されますので、ご安心いただけますと幸いです。メールが届かない携帯キャリアメール ezweb.ne.jp などをご利用されている場合、メール設定等によってはHEXAからの自動メールや認証メールが弾かれて届かないことがあるようです。キャリアメール設定をご確認いただくか、別のメールアドレスをご使用いただきますようお願いいたします。販売終了後に再出品ボタンが出てこない販売終了後、再出品ボタンが出現するまで最大15分程度かかります。少々お待ちください。海外から購入できますか？海外で発行されているクレジットカードでもご購入いただけます。国内クレジットカードと同様、3Dセキュア認証が設定されていない場合はエラーとなります。発行申請時には著作権に加えて商標にも注意してくださいNFT化コンテンツは、写真・イラスト等いかなる作品でも、著作権に加えて商標にもご注意ください。著作権的にはOKでも、シルエットや形状が商標侵害に該当するケースがございます。審査で全て確認はできませんので、発行者様にて100%権利を保有されているものをご申請くださいOpen Seaとの連携についてHEXA NFT MATICについてOpen Seaとの自動連携がOpen Sea側の都合により停止となっております。NFTはブロックチェーンのリンクから確認できます。NFT自体に問題が起きてることはありませんので、ご安心ください。なお、Open Seaとの連携停止についてはこちらをご確認ください。また、それに伴いOncyberはNFTをブロックチェーン情報ではなくOpen Seaのサーバーから情報取得して表示されているため、出庫されてもOncyberで表示されなくなっております。AI生成コンテンツについてAI生成コンテンツについて、生成アプリ側で著作権を明確に主張されていないケースでも、AIによってはウェブ上の著作物を学習データにして生成されているケースがあります。こちらは各国によって判断は異なり、日本では問題ないとされるケースが多いようですが、NFTの特性上、ウォレットにNFTを出庫してほかのプラットフォームで転売が可能となります。国によってはAIの種類によっては今後規制される可能性もありますので、HEXA側で適法性への懸念がわかるものについては今後NGとさせていただきます。ただし、HEXAでは明らかな著作物や商標を含むもののみ審査にて確認させていただいておりますので、前提としては利用規約に基づき、発行者様の責任においてNFT化する権利を100%保有されているもののみ発行申請をいただけますと幸いです。HEXAではスマホアプリは提供しておりませんHEXAではAndroidやiPhoneアプリは提供しておりませんのでご注意ください。HEXAと名の付くスマホアプリとは一切関係ございません。HEXAのサービスはNFTマーケットプレイスHEXA、HEXAメタバース（α）です。ツイートされる際のおすすめタグ付け・ハッシュタグ①HEXAで初めてNFTを販売される時「@HEXANFT #HEXANFT #HEXAデビュー」。②HEXAについて何かツイートされる時「@HEXANFT #HEXANFT」。③HEXAメタバースの部屋を紹介される時「@HEXANFT #HEXANFT #HEXAメタバース」

@法律顧問：AZX総合法律事務所電気通信事業者届出番号：A-04-20234適格事業者番号：T1010701037553

HEXA NFTとは

運営会社

発行者利用規約

購入者利用規約

コミュニティサービス利用に関する特則

HEXA LAND NFT特則（メタバース）

プライバシーポリシー

特定商取引法に関する表示アフィリエイト連携

HEXALAND広告枠の特則

HEXALAND Genesis審査販売

企業向けNFT活用支援ソリューション

お問い合わせ

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HEXA- Definition & Usage Examples | Dictionary.com

GamesDaily CrosswordWord PuzzleWord FinderAll gamesFeaturedWord of the DaySynonym of the DayWord of the YearNew wordsLanguage storiesAll featuredPop cultureSlangEmojiMemesAcronymsGender and sexualityAll pop cultureWriting tipsGrammar Coach™Writing hubGrammar essentialsCommonly confusedAll writing tipsGamesFeaturedPop cultureWriting tipshexa-a combining form meaning “six,” used in the formation of compound words: hexapartite.Origin of hexa-1Combining form representing Greek héxsixAlso especially before a vowel, hex-. Words Nearby hexa-HewishHewittHewletthewnhexhexa-hexabasichexachloridehexachlorobenzenehexachlorocyclohexanehexachloroethaneDictionary.com Unabridged

Based on the Random House Unabridged Dictionary, © Random House, Inc. 2024How to use hexa- in a sentencehexa-ethyl tetraphosphate, known in the trade as "Killex 100," was used effectually twice as a spray.Northern Nut Growers Association Report of the Proceedings at the Thirty-Eighth Annual Meeting | Northern Nut Growers AssociationAnother of these substances is ellagic acid C14H6O8, a double lactone of a hexa-hydroxy-diphenyldicarboxylic acid.Animal Proteins | Hugh Garner BennettFormin—or, if you insist upon its full name, hexa-methylene-tetramine—is a sugar-like substance with a fish-like smell.Creative Chemistry | Edwin E. SlossonBritish Dictionary definitions for hexa-hexa-combining formsix: hexachord; hexameterOrigin of hexa-1from Greek, from hex sixCollins English Dictionary - Complete & Unabridged 2012 Digital Edition

Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012Browse#aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzAboutCareersShopContact usAdvertise with usCookies, terms, & privacyDo not sell my infoFollow usGet the Word of the Day every day!Sign upBy clicking "Sign Up", you are accepting Dictionary.com Terms & Conditions and Privacy Policies.My account© 2024 Dictionary.com, LLC

Hexadecimal - Wikipedia

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1Representation

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1.1Written representation

1.1.1Distinguishing from decimal

1.1.2Syntax that is always Hex

1.2Other symbols for 10–15 and mostly different symbol sets

1.3Verbal and digital representations

1.4Signs

1.5Hexadecimal exponential notation

2Conversion

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2.1Binary conversion

2.2Other simple conversions

2.3Division-remainder in source base

2.4Conversion through addition and multiplication

2.5Tools for conversion

3Elementary arithmetic

4Real numbers

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4.1Rational numbers

4.2Irrational numbers

4.3Powers

5Cultural history

6Base16 (transfer encoding)

7See also

8References

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Hexadecimal

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AfrikaansالعربيةԱրեւմտահայերէնAzərbaycancaবাংলাBân-lâm-gúБеларускаяБеларуская (тарашкевіца)БългарскиBosanskiBrezhonegCatalàČeštinaCymraegDanskDeutschEestiΕλληνικάEspañolEsperantoEuskaraفارسیFrançaisFryskGaeilgeGalego한국어Հայերենहिन्दीHrvatskiIdoBahasa IndonesiaÍslenskaItalianoעבריתJawaҚазақшаKreyòl ayisyenКыргызчаLatinaLatviešuLingua Franca NovaLa .lojban.LombardMagyarМакедонскиമലയാളംमराठीBahasa MelayuMirandésМонголNederlands日本語Norsk bokmålNorsk nynorskOʻzbekcha / ўзбекчаPolskiPortuguêsRomânăРусскийSesotho sa LeboaShqipSimple EnglishSlovenčinaSlovenščinaСрпски / srpskiSrpskohrvatski / српскохрватскиSuomiSvenskaTagalogதமிழ்ไทยTürkçeУкраїнськаاردوTiếng Việt文言吴语ייִדיש粵語中文

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"Sexadecimal" redirects here. For base 60, see Sexagesimal.

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Complex (2i)

Non-integer (φ)

Asymmetric

Sign-value notation

Non-alphabetic

Aegean

Attic

Aztec

Brahmi

Chuvash

Egyptian

Etruscan

Kharosthi

Prehistoric counting

Proto-cuneiform

Roman

Tally marks

Alphabetic

Abjad

Armenian

Alphasyllabic

Akṣarapallī

Āryabhaṭa

Kaṭapayādi

Coptic

Cyrillic

Geʽez

Georgian

Glagolitic

Greek

Hebrew

List of numeral systemsvte

In mathematics and computing, the hexadecimal (also base-16 or simply hex) numeral system is a positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols, most often the symbols "0"–"9" to represent values 0 to 9, and "A"–"F" (or alternatively "a"–"f") to represent values from ten to fifteen.

Software developers and system designers widely use hexadecimal numbers because they provide a human-friendly representation of binary-coded values. Each hexadecimal digit represents four bits (binary digits), also known as a nibble (or nybble).[1] For example, an 8-bit byte can have values ranging from 00000000 to 11111111 (0 to 255 decimal) in binary form, which can be conveniently represented as 00 to FF in hexadecimal.

In mathematics, a subscript is typically used to specify the base. For example, the decimal value 35,443 would be expressed in hexadecimal as 8A7316. In programming, several notations denote hexadecimal numbers, usually involving a prefix. The prefix 0x is used in C, which would denote this value as 0x8A73.

Hexadecimal is used in the transfer encoding Base16, in which each byte of the plaintext is broken into two 4-bit values and represented by two hexadecimal digits.

Representation[edit]

Written representation[edit]

In most current use cases, the letters A–F or a–f represent the values 10–15, while the numerals 0–9 are used to represent their decimal values.

There is no universal convention to use lowercase or uppercase, so each is prevalent or preferred in particular environments by community standards or convention; even mixed case is used. Seven-segment displays use mixed-case AbCdEF to make digits that can be distinguished from each other.

There is some standardization of using spaces (rather than commas or another punctuation mark) to separate hex values in a long list. For instance, in the following hex dump, each 8-bit byte is a 2-digit hex number, with spaces between them, while the 32-bit offset at the start is an 8-digit hex number.

00000000 57 69 6b 69 70 65 64 69 61 2c 20 74 68 65 20 66

00000010 72 65 65 20 65 6e 63 79 63 6c 6f 70 65 64 69 61

00000020 20 74 68 61 74 20 61 6e 79 6f 6e 65 20 63 61 6e

00000030 20 65 64 69 74 0a

Distinguishing from decimal[edit]

In contexts where the base is not clear, hexadecimal numbers can be ambiguous and confused with numbers expressed in other bases. There are several conventions for expressing values unambiguously. A numerical subscript (itself written in decimal) can give the base explicitly: 15910 is decimal 159; 15916 is hexadecimal 159, which equals 34510. Some authors prefer a text subscript, such as 159decimal and 159hex, or 159d and 159h.

Donald Knuth introduced the use of a particular typeface to represent a particular radix in his book The TeXbook.[2] Hexadecimal representations are written there in a typewriter typeface: 5A3

In linear text systems, such as those used in most computer programming environments, a variety of methods have arisen:

Unix (and related) shells, AT&T assembly language and likewise the C programming language (and its syntactic descendants such as C++, C#, Go, D, Java, JavaScript, Python and Windows PowerShell) use the prefix 0x for numeric constants represented in hex: 0x5A3. Character and string constants may express character codes in hexadecimal with the prefix \x followed by two hex digits: '\x1B' represents the Esc control character; "\x1B[0m\x1B[25;1H" is a string containing 11 characters with two embedded Esc characters.[3] To output an integer as hexadecimal with the printf function family, the format conversion code %X or %x is used.

In XML and XHTML, characters can be expressed as hexadecimal numeric character references using the notation ode;, for instance ’ represents the character U+2019 (the right single quotation mark). If there is no x the number is decimal (thus ’ is the same character).[4]

In Intel-derived assembly languages and Modula-2,[5] hexadecimal is denoted with a suffixed H or h: FFh or 05A3H. Some implementations require a leading zero when the first hexadecimal digit character is not a decimal digit, so one would write 0FFh instead of FFh. Some other implementations (such as NASM) allow C-style numbers (0x42).

Other assembly languages (6502, Motorola), Pascal, Delphi, some versions of BASIC (Commodore), GameMaker Language, Godot and Forth use $ as a prefix: $5A3.

Some assembly languages (Microchip) use the notation H'ABCD' (for ABCD16). Similarly, Fortran 95 uses Z'ABCD'.

Ada and VHDL enclose hexadecimal numerals in based "numeric quotes": 16#5A3#. For bit vector constants VHDL uses the notation x"5A3".[6]

Verilog represents hexadecimal constants in the form 8'hFF, where 8 is the number of bits in the value and FF is the hexadecimal constant.

The Icon and Smalltalk languages use the prefix 16r: 16r5A3

PostScript and the Bourne shell and its derivatives denote hex with prefix 16#: 16#5A3.

Common Lisp uses the prefixes #x and #16r. Setting the variables *read-base*[7] and *print-base*[8] to 16 can also be used to switch the reader and printer of a Common Lisp system to Hexadecimal number representation for reading and printing numbers. Thus Hexadecimal numbers can be represented without the #x or #16r prefix code, when the input or output base has been changed to 16.

MSX BASIC,[9] QuickBASIC, FreeBASIC and Visual Basic prefix hexadecimal numbers with &H: &H5A3

BBC BASIC and Locomotive BASIC use & for hex.[10]

TI-89 and 92 series uses a 0h prefix: 0h5A3

ALGOL 68 uses the prefix 16r to denote hexadecimal numbers: 16r5a3. Binary, quaternary (base-4) and octal numbers can be specified similarly.

The most common format for hexadecimal on IBM mainframes (zSeries) and midrange computers (IBM i) running the traditional OS's (zOS, zVSE, zVM, TPF, IBM i) is X'5A3', and is used in Assembler, PL/I, COBOL, JCL, scripts, commands and other places. This format was common on other (and now obsolete) IBM systems as well. Occasionally quotation marks were used instead of apostrophes.

Syntax that is always Hex[edit]

Sometimes the numbers are known to be Hex.

In URIs (including URLs), character codes are written as hexadecimal pairs prefixed with %: http://www.example.com/name%20with%20spaces where %20 is the code for the space (blank) character, ASCII code point 20 in hex, 32 in decimal.

In the Unicode standard, a character value is represented with U+ followed by the hex value, e.g. U+20AC is the Euro sign (€).

Color references in HTML, CSS and X Window can be expressed with six hexadecimal digits (two each for the red, green and blue components, in that order) prefixed with #: white, for example, is represented as #FFFFFF.[11] CSS also allows 3-hexdigit abbreviations with one hexdigit per component: #FA3 abbreviates #FFAA33 (a golden orange: ).

In MIME (e-mail extensions) quoted-printable encoding, character codes are written as hexadecimal pairs prefixed with =: Espa=F1a is "España" (F1hex is the code for ñ in the ISO/IEC 8859-1 character set).[12])

PostScript binary data (such as image pixels) can be expressed as un-prefixed consecutive hexadecimal pairs: AA213FD51B3801043FBC ...

Any IPv6 address can be written as eight groups of four hexadecimal digits (sometimes called hextets), where each group is separated by a colon (:). This, for example, is a valid IPv6 address: 2001:0db8:85a3:0000:0000:8a2e:0370:7334 or abbreviated by removing leading zeros as 2001:db8:85a3::8a2e:370:7334 (IPv4 addresses are usually written in decimal).

Globally unique identifiers are written as thirty-two hexadecimal digits, often in unequal hyphen-separated groupings, for example 3F2504E0-4F89-41D3-9A0C-0305E82C3301.

Other symbols for 10–15 and mostly different symbol sets[edit]

The use of the letters A through F to represent the digits above 9 was not universal in the early history of computers.

During the 1950s, some installations, such as Bendix-14, favored using the digits 0 through 5 with an overline to denote the values 10–15 as 0, 1, 2, 3, 4 and 5.

The SWAC (1950)[13] and Bendix G-15 (1956)[14][13] computers used the lowercase letters u, v, w, x, y and z for the values 10 to 15.

The ORDVAC and ILLIAC I (1952) computers (and some derived designs, e.g. BRLESC) used the uppercase letters K, S, N, J, F and L for the values 10 to 15.[15][13]

The Librascope LGP-30 (1956) used the letters F, G, J, K, Q and W for the values 10 to 15.[16][13]

On the PERM (1956) computer, hexadecimal numbers were written as letters O for zero, A to N and P for 1 to 15. Many machine instructions had mnemonic hex-codes (A=add, M=multiply, L=load, F=fixed-point etc.); programs were written without instruction names.[17]

The Honeywell Datamatic D-1000 (1957) used the lowercase letters b, c, d, e, f, and g whereas the Elbit 100 (1967) used the uppercase letters B, C, D, E, F and G for the values 10 to 15.[13]

The Monrobot XI (1960) used the letters S, T, U, V, W and X for the values 10 to 15.[13]

The NEC parametron computer NEAC 1103 (1960) used the letters D, G, H, J, K (and possibly V) for values 10–15.[18]

The Pacific Data Systems 1020 (1964) used the letters L, C, A, S, M and D for the values 10 to 15.[13]

Bibi-binary

New numeric symbols and names were introduced in the Bibi-binary notation by Boby Lapointe in 1968.

Bruce Alan Martin's hexadecimal notation proposal[19]

Bruce Alan Martin of Brookhaven National Laboratory considered the choice of A–F "ridiculous". In a 1968 letter to the editor of the CACM, he proposed an entirely new set of symbols based on the bit locations.[19]

Ronald O. Whitaker's hexadecimal notation proposal.[20][21]

Ronald O. Whitaker of Rowco Engineering Co., in 1972, proposed a triangular font that allows "direct binary reading" in order to "permit both input and output from computers without respect to encoding matrices."[20][21]

Some seven-segment display decoder chips (i.e., 74LS47) show unexpected output due to logic designed only to produce 0–9 correctly.[22]

Verbal and digital representations[edit]

Since there were no traditional numerals to represent the quantities from ten to fifteen, alphabetic letters were re-employed as a substitute. Most European languages lack non-decimal-based words for some of the numerals eleven to fifteen. Some people read hexadecimal numbers digit by digit, like a phone number, or using the NATO phonetic alphabet, the Joint Army/Navy Phonetic Alphabet, or a similar ad-hoc system. In the wake of the adoption of hexadecimal among IBM System/360 programmers, Magnuson (1968)[23] suggested a pronunciation guide that gave short names to the letters of hexadecimal – for instance, "A" was pronounced "ann", B "bet", C "chris", etc.[23] Another naming-system was published online by Rogers (2007)[24] that tries to make the verbal representation distinguishable in any case, even when the actual number does not contain numbers A–F. Examples are listed in the tables below. Yet another naming system was elaborated by Babb (2015), based on a joke in Silicon Valley.[25]

Others have proposed using the verbal Morse Code conventions to express four-bit hexadecimal digits, with "dit" and "dah" representing zero and one, respectively, so that "0000" is voiced as "dit-dit-dit-dit" (....), dah-dit-dit-dah (-..-) voices the digit with a value of nine, and "dah-dah-dah-dah" (----) voices the hexadecimal digit for decimal 15.

Hexadecimal finger-counting scheme

Systems of counting on digits have been devised for both binary and hexadecimal. Arthur C. Clarke suggested using each finger as an on/off bit, allowing finger counting from zero to 102310 on ten fingers.[26] Another system for counting up to FF16 (25510) is illustrated on the right.

Magnuson (1968)[23]naming method

Number

Pronunciation

ann

bet

chris

dot

ernest

frost

annteen

annty

fifty-bet

A01C

annty christeen

1AD0

annteen dotty

3A7D

thirty-ann seventy-dot

Rogers (2007)[24] naming method

Number

Pronunciation

ten

eleven

twelve

draze

eptwin

fim

tex

oneteek

fimteek

fiftek

twelftek

100

hundrek

1000

thousek

thirtek-eptwin

eptek-one

C4A

twelve-hundrek-fourtek-ten

1743

one-thousek-seven--hundrek-fourtek-three

Signs[edit]

The hexadecimal system can express negative numbers the same way as in decimal: −2A to represent −4210 and so on.

Hexadecimal can also be used to express the exact bit patterns used in the processor, so a sequence of hexadecimal digits may represent a signed or even a floating-point value. This way, the negative number −4210 can be written as FFFF FFD6 in a 32-bit CPU register (in two's-complement), as C228 0000 in a 32-bit FPU register or C045 0000 0000 0000 in a 64-bit FPU register (in the IEEE floating-point standard).

Hexadecimal exponential notation[edit]

Just as decimal numbers can be represented in exponential notation, so too can hexadecimal numbers. P notation uses the letter P (or p, for "power"), whereas E (or e) serves a similar purpose in decimal E notation. The number after the P is decimal and represents the binary exponent. Increasing the exponent by 1 multiplies by 2, not 16: 20p0 = 10p1 = 8p2 = 4p3 = 2p4 = 1p5. Usually, the number is normalized so that the hexadecimal digits start with 1. (zero is usually 0 with no P).

Example: 1.3DEp42 represents 1.3DE16 × 24210.

P notation is required by the IEEE 754-2008 binary floating-point standard, and can be used for floating-point literals in the C99 edition of the C programming language.[27]

Using the %a or %A conversion specifiers, this notation can be produced by implementations of the printf family of functions following the C99 specification[28] and

Single Unix Specification (IEEE Std 1003.1) POSIX standard.[29]

Conversion[edit]

Binary conversion[edit]

Most computers manipulate binary data, but it is difficult for humans to work with a large number of digits for even a relatively small binary number. Although most humans are familiar with the base 10 system, it is much easier to map binary to hexadecimal than to decimal because each hexadecimal digit maps to a whole number of bits (410).

This example converts 11112 to base ten. Since each position in a binary numeral can contain either a 1 or a 0, its value may be easily determined by its position from the right:

00012 = 110

00102 = 210

01002 = 410

10002 = 810

Therefore:

11112

= 810 + 410 + 210 + 110

= 1510

With little practice, mapping 11112 to F16 in one step becomes easy: see table in written representation. The advantage of using hexadecimal rather than decimal increases rapidly with the size of the number. When the number becomes large, conversion to decimal is very tedious. However, when mapping to hexadecimal, it is trivial to regard the binary string as 4-digit groups and map each to a single hexadecimal digit.[30]

This example shows the conversion of a binary number to decimal, mapping each digit to the decimal value, and adding the results.

(01011110101101010010)2

= 26214410 + 6553610 + 3276810 + 1638410 + 819210 + 204810 + 51210 + 25610 + 6410 + 1610 + 210

= 38792210

Compare this to the conversion to hexadecimal, where each group of four digits can be considered independently, and converted directly:

(01011110101101010010)2

0101

1110

1011

0101

00102

216

5EB5216

The conversion from hexadecimal to binary is equally direct.[30]

Other simple conversions[edit]

Although quaternary (base 4) is little used, it can easily be converted to and from hexadecimal or binary. Each hexadecimal digit corresponds to a pair of quaternary digits and each quaternary digit corresponds to a pair of binary digits. In the above example 5 E B 5 216 = 11 32 23 11 024.

The octal (base 8) system can also be converted with relative ease, although not quite as trivially as with bases 2 and 4. Each octal digit corresponds to three binary digits, rather than four. Therefore, we can convert between octal and hexadecimal via an intermediate conversion to binary followed by regrouping the binary digits in groups of either three or four.

Division-remainder in source base[edit]

As with all bases there is a simple algorithm for converting a representation of a number to hexadecimal by doing integer division and remainder operations in the source base. In theory, this is possible from any base, but for most humans only decimal and for most computers only binary (which can be converted by far more efficient methods) can be easily handled with this method.

Let d be the number to represent in hexadecimal, and the series hihi−1...h2h1 be the hexadecimal digits representing the number.

i ← 1

hi ← d mod 16

d ← (d − hi) / 16

If d = 0 (return series hi) else increment i and go to step 2

"16" may be replaced with any other base that may be desired.

The following is a JavaScript implementation of the above algorithm for converting any number to a hexadecimal in String representation. Its purpose is to illustrate the above algorithm. To work with data seriously, however, it is much more advisable to work with bitwise operators.

function toHex(d) {

var r = d % 16;

if (d - r == 0) {

return toChar(r);

}

return toHex((d - r) / 16) + toChar(r);

}

function toChar(n) {

const alpha = "0123456789ABCDEF";

return alpha.charAt(n);

}

Conversion through addition and multiplication[edit]

A hexadecimal multiplication table

It is also possible to make the conversion by assigning each place in the source base the hexadecimal representation of its place value — before carrying out multiplication and addition to get the final representation.

For example, to convert the number B3AD to decimal, one can split the hexadecimal number into its digits: B (1110), 3 (310), A (1010) and D (1310), and then get the final result by multiplying each decimal representation by 16p (p being the corresponding hex digit position, counting from right to left, beginning with 0). In this case, we have that:

B3AD = (11 × 163) + (3 × 162) + (10 × 161) + (13 × 160)

which is 45997 in base 10.

Tools for conversion[edit]

Many computer systems provide a calculator utility capable of performing conversions between the various radices frequently including hexadecimal.

In Microsoft Windows, the Calculator utility can be set to Programmer mode, which allows conversions between radix 16 (hexadecimal), 10 (decimal), 8 (octal) and 2 (binary), the bases most commonly used by programmers. In Programmer Mode, the on-screen numeric keypad includes the hexadecimal digits A through F, which are active when "Hex" is selected. In hex mode, however, the Windows Calculator supports only integers.

Elementary arithmetic[edit]

Elementary operations such as addition, subtraction, multiplication and division can be carried out indirectly through conversion to an alternate numeral system, such as the commonly-used decimal system or the binary system where each hex digit corresponds to four binary digits.

Alternatively, one can also perform elementary operations directly within the hex system itself — by relying on its addition/multiplication tables and its corresponding standard algorithms such as long division and the traditional subtraction algorithm.

Real numbers[edit]

Rational numbers[edit]

As with other numeral systems, the hexadecimal system can be used to represent rational numbers, although repeating expansions are common since sixteen (1016) has only a single prime factor: two.

For any base, 0.1 (or "1/10") is always equivalent to one divided by the representation of that base value in its own number system. Thus, whether dividing one by two for binary or dividing one by sixteen for hexadecimal, both of these fractions are written as 0.1. Because the radix 16 is a perfect square (42), fractions expressed in hexadecimal have an odd period much more often than decimal ones, and there are no cyclic numbers (other than trivial single digits). Recurring digits are exhibited when the denominator in lowest terms has a prime factor not found in the radix; thus, when using hexadecimal notation, all fractions with denominators that are not a power of two result in an infinite string of recurring digits (such as thirds and fifths). This makes hexadecimal (and binary) less convenient than decimal for representing rational numbers since a larger proportion lie outside its range of finite representation.

All rational numbers finitely representable in hexadecimal are also finitely representable in decimal, duodecimal and sexagesimal: that is, any hexadecimal number with a finite number of digits also has a finite number of digits when expressed in those other bases. Conversely, only a fraction of those finitely representable in the latter bases are finitely representable in hexadecimal. For example, decimal 0.1 corresponds to the infinite recurring representation 0.19 in hexadecimal. However, hexadecimal is more efficient than duodecimal and sexagesimal for representing fractions with powers of two in the denominator. For example, 0.062510 (one-sixteenth) is equivalent to 0.116, 0.0912, and 0;3,4560.

DecimalPrime factors of: base, b = 10: 2, 5;b − 1 = 9: 3

HexadecimalPrime factors of: base, b = 1610 = 10: 2; b − 1 = 1510 = F: 3, 5

Reciprocal

Prime factors

Positional representation(decimal)

Positional representation(hexadecimal)

Prime factors

Reciprocal

1/2

0.5

0.8

1/2

1/3

0.3333... = 0.3

0.5555... = 0.5

1/3

1/4

0.25

0.4

1/4

1/5

0.2

0.3

1/5

1/6

2, 3

0.16

0.2A

2, 3

1/6

1/7

0.142857

0.249

1/7

1/8

0.125

0.2

1/8

1/9

0.1

0.1C7

1/9

1/10

2, 5

0.1

0.19

2, 5

1/A

1/11

0.09

0.1745D

1/B

1/12

2, 3

0.083

0.15

2, 3

1/C

1/13

0.076923

0.13B

1/D

1/14

2, 7

0.0714285

0.1249

2, 7

1/E

1/15

3, 5

0.06

0.1

3, 5

1/F

1/16

0.0625

0.1

1/10

1/17

0.0588235294117647

0.0F

1/11

1/18

2, 3

0.05

0.0E38

2, 3

1/12

1/19

0.052631578947368421

0.0D79435E5

1/13

1/20

2, 5

0.05

0.0C

2, 5

1/14

1/21

3, 7

0.047619

0.0C3

3, 7

1/15

1/22

2, 11

0.045

0.0BA2E8

2, B

1/16

1/23

0.0434782608695652173913

0.0B21642C859

1/17

1/24

2, 3

0.0416

0.0A

2, 3

1/18

1/25

0.04

0.0A3D7

1/19

1/26

2, 13

0.0384615

0.09D8

2, D

1/1A

1/27

0.037

0.097B425ED

1/1B

1/28

2, 7

0.03571428

0.0924

2, 7

1/1C

1/29

0.0344827586206896551724137931

0.08D3DCB

1/1D

1/30

2, 3, 5

0.03

0.08

2, 3, 5

1/1E

1/31

0.032258064516129

0.08421

1/1F

1/32

0.03125

0.08

1/20

1/33

3, 11

0.03

0.07C1F

3, B

1/21

1/34

2, 17

0.02941176470588235

0.078

2, 11

1/22

1/35

5, 7

0.0285714

0.075

5, 7

1/23

1/36

2, 3

0.027

0.071C

2, 3

1/24

Irrational numbers[edit]

The table below gives the expansions of some common irrational numbers in decimal and hexadecimal.

Number

Positional representation

Decimal

Hexadecimal

√2 (the length of the diagonal of a unit square)

1.414213562373095048...

1.6A09E667F3BCD...

√3 (the length of the diagonal of a unit cube)

1.732050807568877293...

1.BB67AE8584CAA...

√5 (the length of the diagonal of a 1×2 rectangle)

2.236067977499789696...

2.3C6EF372FE95...

φ (phi, the golden ratio = (1+√5)/2)

1.618033988749894848...

1.9E3779B97F4A...

π (pi, the ratio of circumference to diameter of a circle)

3.141592653589793238462643383279502884197169399375105...

3.243F6A8885A308D313198A2E03707344A4093822299F31D008...

e (the base of the natural logarithm)

2.718281828459045235...

2.B7E151628AED2A6B...

τ (the Thue–Morse constant)

0.412454033640107597...

0.6996 9669 9669 6996...

γ (the limiting difference between the harmonic series and the natural logarithm)

0.577215664901532860...

0.93C467E37DB0C7A4D1B...

Powers[edit]

Powers of two have very simple expansions in hexadecimal. The first sixteen powers of two are shown below.

Value

Value (Decimal)

10hex

16dec

20hex

32dec

40hex

64dec

80hex

128dec

100hex

256dec

200hex

512dec

2A (210dec)

400hex

1024dec

2B (211dec)

800hex

2048dec

2C (212dec)

1000hex

4096dec

2D (213dec)

2000hex

8192dec

2E (214dec)

4000hex

16,384dec

2F (215dec)

8000hex

32,768dec

210 (216dec)

10000hex

65,536dec

Cultural history[edit]

The traditional Chinese units of measurement were base-16. For example, one jīn (斤) in the old system equals sixteen taels. The suanpan (Chinese abacus) can be used to perform hexadecimal calculations such as additions and subtractions.[31]

As with the duodecimal system, there have been occasional attempts to promote hexadecimal as the preferred numeral system. These attempts often propose specific pronunciation and symbols for the individual numerals.[32] Some proposals unify standard measures so that they are multiples of 16.[33][34]

An early such proposal was put forward by John W. Nystrom in Project of a New System of Arithmetic, Weight, Measure and Coins: Proposed to be called the Tonal System, with Sixteen to the Base, published in 1862.[35]

Nystrom among other things suggested hexadecimal time, which subdivides a day by 16,

so that there are 16 "hours" (or "10 tims", pronounced tontim) in a day.[36]

Look up hexadecimal in Wiktionary, the free dictionary.

The word hexadecimal is first recorded in 1952.[37] It is macaronic in the sense that it combines Greek ἕξ (hex) "six" with Latinate -decimal.

The all-Latin alternative sexadecimal (compare the word sexagesimal for base 60) is older, and sees at least occasional use from the late 19th century.[38]

It is still in use in the 1950s in Bendix documentation.

Schwartzman (1994) argues that use of sexadecimal may have been avoided because of its suggestive abbreviation to sex.[39]

Many western languages since the 1960s have adopted terms equivalent in formation to hexadecimal (e.g. French hexadécimal, Italian esadecimale, Romanian hexazecimal, Serbian хексадецимални, etc.)

but others have introduced terms which substitute native words for "sixteen" (e.g. Greek δεκαεξαδικός, Icelandic sextándakerfi, Russian шестнадцатеричной etc.)

Terminology and notation did not become settled until the end of the 1960s.

Donald Knuth in 1969 argued that the etymologically correct term would be senidenary, or possibly sedenary, a Latinate term intended to convey "grouped by 16" modelled on binary, ternary and quaternary etc.

According to Knuth's argument, the correct terms for decimal and octal arithmetic would be denary and octonary, respectively.[40]

Alfred B. Taylor used senidenary in his mid-1800s work on alternative number bases, although he rejected base 16 because of its "incommodious number of digits".[41][42]

The now-current notation using the letters A to F establishes itself as the de facto standard beginning in 1966, in the wake of the

publication of the Fortran IV manual for IBM System/360, which (unlike earlier variants of Fortran) recognizes a standard for entering hexadecimal constants.[43]

As noted above, alternative notations were used by NEC (1960) and The Pacific Data Systems 1020 (1964). The standard adopted by IBM seems to have become widely adopted by 1968, when Bruce Alan Martin

in his letter to the editor of the CACM complains that

With the ridiculous choice of letters A, B, C, D, E, F as hexadecimal number symbols adding to already troublesome problems of distinguishing octal (or hex) numbers from decimal numbers (or variable names), the time is overripe for reconsideration of our number symbols. This should have been done before poor choices gelled into a de facto standard!

Martin's argument was that use of numerals 0 to 9 in nondecimal numbers "imply to us a base-ten place-value scheme":

"Why not use entirely new symbols (and names) for the seven or fifteen nonzero digits needed in octal or hex. Even use of the letters A through P would be an improvement, but entirely new symbols could reflect the binary nature of the system".[19]

He also argued that "re-using alphabetic letters for numerical digits represents a gigantic backward step from the invention of distinct, non-alphabetic glyphs for numerals sixteen centuries ago" (as Brahmi numerals, and later in a Hindu–Arabic numeral system),

and that the recent ASCII standards (ASA X3.4-1963 and USAS X3.4-1968)

"should have preserved six code table positions following the ten decimal digits

-- rather than needlessly filling these with punctuation characters"

(":;<=>?") that might have been placed elsewhere among the 128 available positions.

Base16 (transfer encoding)[edit]

Base16 (as a proper name without a space) can also refer to a binary to text encoding belonging to the same family as Base32, Base58, and Base64.

In this case, data is broken into 4-bit sequences, and each value (between 0 and 15 inclusively) is encoded using one of 16 symbols from the ASCII character set. Although any 16 symbols from the ASCII character set can be used, in practice the ASCII digits '0'–'9' and the letters 'A'–'F' (or the lowercase 'a'–'f') are always chosen in order to align with standard written notation for hexadecimal numbers.

There are several advantages of Base16 encoding:

Most programming languages already have facilities to parse ASCII-encoded hexadecimal

Being exactly half a byte, 4-bits is easier to process than the 5 or 6 bits of Base32 and Base64 respectively

The symbols 0–9 and A–F are universal in hexadecimal notation, so it is easily understood at a glance without needing to rely on a symbol lookup table

Many CPU architectures have dedicated instructions that allow access to a half-byte (otherwise known as a "nibble"), making it more efficient in hardware than Base32 and Base64

The main disadvantages of Base16 encoding are:

Space efficiency is only 50%, since each 4-bit value from the original data will be encoded as an 8-bit byte. In contrast, Base32 and Base64 encodings have a space efficiency of 63% and 75% respectively.

Possible added complexity of having to accept both uppercase and lowercase letters

Support for Base16 encoding is ubiquitous in modern computing. It is the basis for the W3C standard for URL percent encoding, where a character is replaced with a percent sign "%" and its Base16-encoded form. Most modern programming languages directly include support for formatting and parsing Base16-encoded numbers.

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What is Hexadecimal Numbers System? Table, Conversions, Examples

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Hexadecimal - Wikipedia

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What is Hexadecimal Numbers System? Table, Conversions, Examples

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HEXA - Wikipedia

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HEXA（ヘキサ） - ヘキサ（HEXA）NFTマーケットプレイス

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Color Hex - ColorHexa.com

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Hexadecimal - Wikipedia

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