What is a number System?

 Number System

A number system is a way of writing down numbers. In our everyday decimal system, we represent numbers in the form 434.15, for example. Digits within the number indicate units, tens, hundreds, tenths, hundredths, thousandths and so on, and are called coefficients. So 434.15 = (4 × 100) + (3 × 10) + (4 × 1) + (1/10) + (5/100) . This is simply a shorthand description of a sum of powers of ten, and any real number can be written in this way.

But there is nothing special about this “base 10” system. The same number can be written in any positive whole-number base n, using coefficients ranging from 0 up to n - 1. For example, in base two or binary, the number 8^5/16 can be written as 1000.0101. The coefficients to the left of the decimal point show units, twos, fours, and eights—powers of 2. Those to the right show halves, quarters, eighths, and sixteenths. Most computers use the binary system, since two coefficients (0 and 1) are easier to work with electronically.