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AQA GCSE Computer Science

Data representation: binary, hex, images and sound — AQA GCSE Computer Science revision

Free revision notes, key terms, common exam traps and 5 practice questions with answers. About 7 minutes to read.

Binary, denary and hexadecimal

  • Computers store all data as binary (base 2), using only 0s and 1s, because circuits have two reliable states: on and off.
  • A bit is a single binary digit; a nibble is 4 bits; a byte is 8 bits, the standard unit for a single character.
  • To convert binary to denary, add the place values (128, 64, 32, 16, 8, 4, 2, 1) where there is a 1.
  • Hexadecimal (base 16) uses digits 0-9 and letters A-F; each hex digit represents exactly 4 binary bits (a nibble), so a byte is 2 hex digits.
  • Hex is used to represent large binary values (e.g. colours, MAC addresses) more compactly and readably than binary.

Binary arithmetic

  • Binary addition follows: 0+0=0, 0+1=1, 1+1=10 (0 carry 1), 1+1+1=11 (1 carry 1).
  • An overflow error occurs when the result of a binary addition needs more bits than the register/storage allows.
  • A binary shift moves all bits left or right by a number of places; a left shift by n multiplies the value by 2^n, a right shift by n divides by 2^n (for unsigned integers).
  • Binary shifts are a fast way for computers to perform multiplication/division by powers of two.

Key terms

Bit
A single binary digit, 0 or 1.
Nibble
A group of 4 bits.
Byte
A group of 8 bits, the standard unit for one character.
Hexadecimal
Base 16 number system using digits 0-9 and A-F.
Binary shift
Moving all bits in a binary number left or right.
Overflow
Error when a calculation result needs more bits than are available.

Common exam traps

  • Forgetting binary place values start at 1 (rightmost) and double each place moving left: 1,2,4,8,16,32,64,128.
  • Miscounting hex digits — each hex digit is exactly 4 bits, so an 8-bit byte is always 2 hex digits.
  • Confusing bits and bytes when calculating file sizes — always check which unit is being asked for and convert (÷8) when needed.

Practice questions with answers

  1. 1. How many bits are in a byte?

    • • 4
    • • 8
    • • 16
    • • 32

    Answer: 8

    A byte is defined as 8 bits.

  2. 2. How many bits are in a nibble?

    • • 2
    • • 4
    • • 8
    • • 16

    Answer: 4

    A nibble is half a byte, or 4 bits.

  3. 3. Convert the binary number 1011 to denary.

    Answer: 11

    8+0+2+1 = 11 (place values 8,4,2,1).

  4. 4. Convert the binary number 11001100 to denary.

    Answer: 204

    128+64+0+0+8+4+0+0 = 204.

  5. 5. Convert the denary number 25 to 8-bit binary.

    Answer: 00011001

    16+8+1 = 25, so bits set at 16, 8 and 1: 00011001.

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