Binary and data representation - EdexcelHexadecimal notation

In computer science, different number bases are used:

• denary is base 10, which has ten symbols (0-9)
• binary is base 2 , which has two symbols (0-1)

Hexadecimal, also known as hex, is the third commonly-used number system and is base 16. It has 16 symbols - 0-9 and the capital letters A, B, C, D, E and F.

Hexadecimal is useful because large numbers can be represented using fewer digits. For example, colour values and MAC addresses are often represented in hexadecimal.

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.

Converting between binary and hexadecimal

The simplest way to convert from binary to hexadecimal, and vice versa, is to split the binary number into nibbles (four bits) first, then convert each nibble to hexadecimal. A nibble can hold 16 values in its 4 bits so is useful for converting hexadecimal.

Binary to hexadecimal

1. Start at the rightmost digit and break the binary number into nibbles.
2. Next, convert each nibble into hexadecimal
3. Put the hexadecimal digits together.

Example: 11000011 to hexadecimal

Break into nibbles: 1100 0011.

1100 = hexadecimal C and 0011 = hexadecimal 3. Remember, this is hexadecimal base 16 symbol 3, not denary symbol 3.

Result: C3

Example: 00110011 to hexadecimal

Break into nibbles: 0011 0011.

0011 = hexadecimal 3 and 0011 = hexadecimal 3

Result: 33

Hexadecimal to binary

1. Split the hexadecimal number into individual digits.
2. Convert each hexadecimal digit into its binary equivalent (a nibble).
3. Combine the nibbles to make one binary number.

Example: hexadecimal 28 to binary

2 = binary 0010 and 8 = binary 1000

Result: 00101000

Example: hexadecimal FC to binary

F = binary 1111 and C = binary 1100

Result: 11111100