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Binary basics: bits and place value
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Everything a computer stores, from numbers to music, is held as binary: just 0s and 1s. This starter gets you counting in binary before the full binary lessons.
Why binary?
Inside a computer are billions of tiny switches called transistors. Each one is either on (1) or off (0).
Two states are easy to build and reliable, so computers store everything in binary (base 2).
One binary digit is a bit.
Two states are easy to build and reliable, so computers store everything in binary (base 2).
One binary digit is a bit.
Place values
In denary (base 10) the columns are 1, 10, 100... In binary the columns double each time, from the right.
How many values?
Each extra bit doubles the number of patterns.
n bits give 2n different values.
4 bits: 24 = 16 values, from 0 to 15.
8 bits (a byte): 28 = 256 values, from 0 to 255.
n bits give 2n different values.
4 bits: 24 = 16 values, from 0 to 15.
8 bits (a byte): 28 = 256 values, from 0 to 255.
Convert 13 to 4-bit binary.
- Place values: 8, 4, 2, 1.
- 13 = 8 + 4 + 1, so put 1 under 8, 4 and 1, and 0 under 2.
Answer: 1101
Computers use binary because transistors have two states. Binary place values double from the right: 1, 2, 4, 8, 16... n bits give 2n values, from 0 to 2n minus 1.
The interactive lesson includes the diagrams for this topic.
Check you have got it
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