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Binary numbers
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Computers store everything as 1s and 0s. Converting between binary and denary is a guaranteed exam skill.
Why binary?
Computers use transistors that are either on (1) or off (0).
One binary digit is a bit. Eight bits make a byte. Four bits make a nibble.
One binary digit is a bit. Eight bits make a byte. Four bits make a nibble.
Binary to denary
Write the place values above each bit, then add the columns with a 1.
Denary to binary
Work from the left. If the place value fits, write 1 and subtract it.
200: 128 fits (72 left), 64 fits (8 left), 32 no, 16 no, 8 fits (0 left), then 0s.
200 = 11001000
The largest 8-bit unsigned number is 11111111 = 255.
200: 128 fits (72 left), 64 fits (8 left), 32 no, 16 no, 8 fits (0 left), then 0s.
200 = 11001000
The largest 8-bit unsigned number is 11111111 = 255.
Convert 10010110 to denary.
- Place values with a 1: 128, 16, 4 and 2.
- 128 + 16 + 4 + 2 = 150
Answer: 150
Place values 128, 64, 32, 16, 8, 4, 2, 1. Binary to denary: add the columns with a 1. Denary to binary: subtract the biggest value that fits, from the left. 8 bits hold 0 to 255.
The interactive lesson includes the diagrams for this topic.
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