#MathsInMinutes Day 6: Number Systems

● 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 X 100) + (3 X 10) + (4 X 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 coefficient to the left of the decimal point shows units, twos, fours and eights – powers of two. Those to the right show halves, quarters, eights and sixteenths.

● Most computers use the binary system, since two coefficients (0 and 1) are easier to work with electronically.

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