Converting Between Hexadecimal & Binary (Edexcel GCSE Computer Science)

The Use of Hexadecimal in Computing

Why is hexadecimal used?

• In Computer Science hexadecimal is often preferred when working with large values

• It takes fewer digits to represent a given value in hexadecimal than in binary

  • 1 hexadecimal digit corresponds 4 bits (one nibble) and can represent 16 unique values (0-F)

• It is beneficial to use hexadecimal over binary because:

  • The more bits there are in a binary number, the harder it makes for a human to read

  • Numbers with more bits are more prone to errors when being copied

• Examples of where hexadecimal can be seen:

  • MAC addresses

  • Colour values

• A typical MAC address consists of 12 hexadecimal digits, equivalent to 48 digits in in binary

  • AA:BB:CC:DD:EE:FF

  • 10101010:10111011:11001100:11011101:11101110:11111111

• Writing down or performing calculations with 48 binary digits makes it very easy to make a mistake

• A typical hexadecimal colour code consists of 6 hexadecimal digits, equivalent to 24 digits in binary

  • #66FF33 (green)

  • 01000010:11111111:00110011

Hexadecimal to Binary Conversion

How do you convert from hexadecimal to binary?

Example 1

• To convert the hexadecimal number 5F to binary, first split the digits apart and convert each to a binary nibble (4 bits)

• Join the 2 binary nibbles together to create an 8 bit binary number

• Hexadecimal 5F is 01011111 in binary

Example 2

• To convert the hexadecimal number 26 to binary, first split the digits apart and convert each to a binary nibble (4 bits)

• Join the 2 binary nibbles together to create an 8 bit binary number

• Hexadecimal 26 is 00100101 in binary

Binary to Hexadecimal Conversion

How do you convert from binary to hexadecimal?

Example 1

• To convert the binary number 10110111 to hexadecimal, first split the 8 bit number into 2 binary nibbles

• For each nibble, convert the binary to it’s denary value

• (1 x 8) + (1 x 2) + (1 x 1) = 11 (B)

• (1 x 4) + (1 x 2) + (1 x 1) = 7

• Join them together to make a 2 digit hexadecimal number

• Binary 10110111 is B7 in hexadecimal

Example 2

• To convert the binary number 00111001 to hexadecimal, first split the 8 bit number into 2 binary nibbles

• For each nibble, convert the binary to it’s denary value

• (1 x 2) + (1 x 1) = 3

• (1 x 8) + (1 x 1) = 9

• Join them together to make a 2 digit hexadecimal number

• Binary 00111001 is 39 in hexadecimal