Inside a computer, everything is stored as tiny switches that are either off or on. Call them 0 and 1. One of these is a bit (binary digit). Two states are easy to build reliably out of electricity, which is why computers use them rather than ten.
We count in base 10: each place is worth ten times the one to its right (ones, tens, hundreds). Binary is base 2: each place is worth twice the one to its right, so the places are 1, 2, 4, 8, 16, 32, 64, 128 and so on.
To read a binary number, add up the places that have a 1. 1011 is 8 + 0 + 2 + 1 = 11. 11111111 is 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255.
To write a number in binary, take the biggest place that fits, subtract it, and repeat. 13 is 8 + 4 + 1, so it's 1101. Another way: keep dividing by 2 and write down the remainders, then read them from the bottom up.
Each extra bit doubles how many values you can store. With n bits you can count from 0 up to 2ⁿ - 1: 8 bits give 256 values (0 to 255), 16 bits give 65,536.
What is binary 101 in ordinary numbers?
| Bit | One binary digit: 0 or 1. |
|---|---|
| Place values | 1, 2, 4, 8, 16, 32, 64, 128… |
| n bits | 2ⁿ values, from 0 to 2ⁿ - 1. |
| 0b1011 | How Python and many languages write binary. |