Presently, all digital computers rely on the binary number system. The
simple reason is that present-day technology allows to
store information reliably only by turning something on or off or
on a CD to make a small indentation into the surface or not.
Mathematically we state this in terms of a zero (0) or a (1) and call a storage unit which can change its state between 0 and 1 a "bit". Eight consecutive (in memory) bits are called a byte and all computations computers perform are conducted in terms of this binary ( 0 and 1 ) number system.
How does it work ? Well, there are a lot of similarities
between the usual decimal and the binary system :
In the decimal system, when we count some things and write as we count, we would write down all the non-zero digits ( 1, 2, ..., 9) and once we have exhausted the non-zero digits we proceed with a 1 infront of a 0 ( as in 10 ). Then we keep on playing with the non-zero digits as we keep on counting until we reach 99 and then 100, again adding a zero.
In the binary system we do the same keeping in mind that we have only a single non-zero digit, namely the 1. As a consequence the decimal numbers one through nine become :