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Hexadecimal

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  • Most Western cultures use the decimal system (base 10) to represent numeric data.

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  • As we know, computers use the binary system (base 2) to represent numeric (and indeed all) data.

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  • As computer scientists, it’s useful to be able to express data the same way the computer does, but trying to parse a big chain of 0s and 1s can be annoying.

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  • The hexadecimal system (base 16) is a much more concise way to express data on a computer system.

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0 1 2 3 4 5 6 7 8 9 a b c d e f

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  • Hexadecimal makes it so that a group of four binary digits (bits) can be expressed with a single character, since there are 16 possible combinations of 4 bits (0 or 1).

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Decimal

Binary

Hex

​

Decimal

Binary

Hex

0

0000

0

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8

1000

8

1

0001

1

​

9

1001

9

2

0010

2

​

10

1010

a

3

0011

3

​

11

1011

b

4

0100

4

​

12

1100

c

5

0101

5

​

13

1101

d

6

0110

6

​

14

1110

e

7

0111

7

​

15

1111

f

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Decimal

Binary

Hex

​

Decimal

Binary

Hex

0

0000

0x0

​

8

1000

0x8

1

0001

0x1

​

9

1001

0x9

2

0010

0x2

​

10

1010

0xa

3

0011

0x3

​

11

1011

0xb

4

0100

0x4

​

12

1100

0xc

5

0101

0x5

​

13

1101

0xd

6

0110

0x6

​

14

1110

0xe

7

0111

0x7

​

15

1111

0xf

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  • To convert a binary number to hexadecimal, group four bits together from right to left, padding the leftmost group with extra 0s at the front if necessary.

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  • To convert a binary number to hexadecimal, group four bits together from right to left, padding the leftmost group with extra 0s at the front if necessary.

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01000110101000101011100100111101

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  • To convert a binary number to hexadecimal, group four bits together from right to left, padding the leftmost group with extra 0s at the front if necessary.

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01000110101000101011100100111101

0100 0110 1010 0010 1011 1001 0011 1101

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  • To convert a binary number to hexadecimal, group four bits together from right to left, padding the leftmost group with extra 0s at the front if necessary.

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01000110101000101011100100111101

0100 0110 1010 0010 1011 1001 0011 1101

4 6 A 2 B 9 3 D

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  • To convert a binary number to hexadecimal, group four bits together from right to left, padding the leftmost group with extra 0s at the front if necessary.

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01000110101000101011100100111101

0100 0110 1010 0010 1011 1001 0011 1101

4 6 A 2 B 9 3 D

0x46A2B93D