Data representation - EduqasHexadecimal

In computer science, different number bases are used to represent numbers:

• denary is base 10, which has ten symbols (0,1,2,3,4,5,6,7,8,9)
• binary is base 2 , which has two symbols (0,1)

Hexadecimal, also known as hex, is also used. It has 16 symbols – the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 and the capital letters A, B, C, D, E and F.

Hexadecimal is useful because large numbers can be represented using fewer digits.

Additionally, hexadecimal is easier to understand than binary. Programmers often use hexadecimal to represent binary values as they are simpler to write and check than when using binary.

Hexadecimal to denary

Whereas denary place values are powers of 10, and binary place values are powers of 2, hexadecimal place values are powers of 16. The first five hexadecimal place values are 65,536, 4,096, 256, 16 and 1.

Each place value can be represented by the symbols 0 through to F.

To convert hexadecimal to denary, take each place value that has a unit in it and add them together.

Example - hexadecimal 7C

Result: (7 × 16) + (C × 1) = (7 × 16) + (12 × 1) = (112) + (12) = 124

Denary to hexadecimal

• If the denary number is bigger than 16, divide it by 16. Take the hexadecimal equivalent of this result - this represents the first digit. Take the hexadecimal equivalent of the remainder - this represents the second digit.
• If the denary number is smaller than 16, take the hexadecimal equivalent of the denary number.

Example - convert denary 22 to hexadecimal

16 goes into 22 once with 6 left over, so 22 ÷ 16 = 1 remainder 6

1 = hexadecimal 1

6 = hexadecimal 6

Result: 16

Example - convert denary 138 to hexadecimal

138 ÷ 16 = 8 remainder 10

8 = hexadecimal 8

10 = hexadecimal A

Result: 8A