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Binary numbers
Years 5 to 11
Computers count with only 0 and 1, and every number can be built from doubling place values.
For learners
Computers store everything with switches that are either off or on. We write off as 0 and on as 1. This way of counting is called binary.
In our usual numbers, each place is worth ten times the one to its right. In binary, each place is worth double: 1, 2, 4, 8, 16, and so on.
To read a binary number, add up the place values that have a 1. The binary number 1101 has a 8, a 4 and a 1, so it is 8 + 4 + 1 = 13.
A worked example
What is the binary number 10110 in ordinary numbers?
- The place values are 16, 8, 4, 2, 1.
- The ones are under 16, 4 and 2.
- .
For grown-ups
Binary is place value with a base of 2 instead of 10. Write the doubling place values above the digits and add the ones. To convert a number to binary, find the biggest place value that fits, write a 1, take it away, and carry on down. Everything on a computer, from text to music, is stored as long strings of bits.
Common mistakes
- Reading the place values from the wrong end.
- Forgetting that a 0 still takes up a place.
- Thinking 1 + 1 = 2 in binary (it is 10, which means one 2 and no 1s).
Why it matters
Every photo, song, game and message on a phone or computer is stored as bits, which are binary digits.
Topics in quarter that use this
- Binary numbers
- Hexadecimal and colours
- Storage and file sizes