GCSE > Computer Science > OCR > GCSE Computer Science > COMPUTER SYSTEMS: Number systems > Converting denary and binary
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  • Binary is base-2 (0s and 1s). 8-bit binary is 8 digits (e.g. 13 = 00001101). We convert by finding powers of 2 that add up to the number.
  • For example, to convert the denary number 88 to binary:
  1. Start with the largest number that can be subtracted from 88 and give a positive integer (i.e. 88 – 64 = 24) and put a 1 in that column.
  2. Take the remainder (24) and see if the next column can be subtracted from it (i.e. 24 – 32). This would be a negative number, so put a 0 in that column and move to the next one.
  3. Repeat for the next column (24 – 16 = 8). This is positive, so put a 1.
  4. Continue until there is no remainder (8 – 8 = 0) and put 0s for any remaining columns.
  5. You can check your result by adding the place values for all columns with a 1 (i.e. 64 + 16 + 8 = 88 ✔️).
Place values 128 64 32 16 8 4 2 1
Binary 0 1 0 1 1 0 0 0
  • To convert a binary number to denary, add up all place values with a 1: 
    • E.g. 10010111 = 128 0 0 + 16 0 + 4 + 2 + 1 = 151
    • E.g. 00111100 = 0 0 32 + 16 + 8 + 4 0 0 = 60
    • E.g. 11111111 = 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255

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