Hexadecimal

What you need to know

• ✓The hex digits are 0–9, then A = 10, B = 11, C = 12, D = 13, E = 14 and F = 15.
• ✓Explain why hexadecimal is used: it's a shorter way for people to write and read binary. The computer itself still stores and processes everything in binary.
• ✓Convert in both directions between binary and hex, and between denary and hex, for values from 0 to 255 (00 to FF in hex).
• ✓To go from binary to hex, split the 8 bits into two groups of four and turn each group into one hex digit.
• ✓In a two-digit hex number, the left digit counts 16s and the right digit counts 1s.

What you don’t need

• Hex numbers longer than two digits: the largest you'll be asked to convert is FF, which is 255.
• The word “nibble” for a group of four bits is a common teaching term, but it isn't in AQA's specification — you won't be required to use it.

Worked examples

1. Explain why hexadecimal is often used in computer science. (2 marks)

   Answer: One mark for saying hex is a shorter, more compact way of writing a binary value, so it's easier for people to read. One mark for saying the computer still stores and processes the data in binary — hex is only for people.

2. Convert the 8-bit binary number 1101 0110 into hexadecimal.

   1. Split it into two groups of four: 1101 and 0110.
   2. 1101 = 8 + 4 + 1 = 13, which is the hex digit D.
   3. 0110 = 4 + 2 = 6.

   Answer: D6

3. Convert the hexadecimal number 9E into binary, and then into denary.

   1. Turn each hex digit into four bits: 9 = 1001, and E (14) = 1110.
   2. So 9E = 1001 1110.
   3. Add up the place values with a 1: 128 + 16 + 8 + 4 + 2 = 158.
   4. Check: 9 × 16 + 14 = 158.

   Answer: 1001 1110, which is 158

4. Convert the denary number 75 into hexadecimal.

   1. Convert to binary first: 75 = 64 + 8 + 2 + 1 = 0100 1011.
   2. Split into two groups of four: 0100 = 4 and 1011 = 11, which is B.
   3. Check: 4 × 16 + 11 = 75.

   Answer: 4B

Common mistakes

• ✕Writing a value from 10 to 15 as two digits — for example, writing 1010 as “10” instead of A.
• ✕Splitting the bits before writing all eight. Pad to 8 bits first, then split into two groups of four, or every digit after a dropped zero shifts.
• ✕Saying that computers use hexadecimal. They don't: hex is a shorthand for people, and the computer works in binary.