Binary Numbers and Bits
Why does a computer count with only 0 and 1?
Summary
Inside a computer there are billions of tiny switches, and each one is either on or off: 1 or 0. This single piece of information is called a bit. Line bits up and, like the digits of an ordinary number, each one is worth twice the one before, so any number can be written. Letters, colours and sounds are also stored in the end as strings of bits.
In depth
In the decimal system each place is worth 10 times the one before; in binary it is worth twice as much: 1, 2, 4, 8, 16… That is why 8 bits (one byte) can take 2⁸ = 256 different values. Gottfried Leibniz described binary numbers in detail in 1703; in 1937 Claude Shannon showed that this logic could be built with electrical circuits, opening the way to the modern computer. Because long strings of bits are hard to read, programmers use hexadecimal: every 4 bits correspond to a single digit (0–9, A–F). A limited number of bits means a limited number of values; when a number does not fit it overflows and wraps around. Negative numbers are written with "two's complement", by giving the leftmost bit a negative value.
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