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Converting denary to binary
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You can already turn binary into denary. Now go the other way, and see why the two systems match.
The subtraction method
Write the place values: 128, 64, 32, 16, 8, 4, 2, 1.
Starting from the left, ask: does this place value fit into what is left?
If yes, write 1 and subtract it. If no, write 0.
Carry on until you reach the 1s column.
Starting from the left, ask: does this place value fit into what is left?
If yes, write 1 and subtract it. If no, write 0.
Carry on until you reach the 1s column.
Example: 45
128? No: 0. 64? No: 0. 32? Yes: 1, leaving 13. 16? No: 0. 8? Yes: 1, leaving 5. 4? Yes: 1, leaving 1. 2? No: 0. 1? Yes: 1.
Check your answer
Always convert back: 32 + 8 + 4 + 1 = 45. Correct.
Use all 8 bits, with 0s at the front if needed.
Odd numbers always end in 1; even numbers always end in 0.
Use all 8 bits, with 0s at the front if needed.
Odd numbers always end in 1; even numbers always end in 0.
Convert 100 to 8-bit binary.
- 64 fits: 100 - 64 = 36.
- 32 fits: 36 - 32 = 4.
- 4 fits: 4 - 4 = 0.
- So 1s go under 64, 32 and 4.
Answer: 01100100
To convert denary to binary, work from 128 down to 1: write 1 and subtract when the place value fits, otherwise write 0. Check by adding back.
The interactive lesson includes the diagrams for this topic.
Check you have got it
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