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Floating point

computer format for representing real numbers

Real numbers in binary have to be stored in a special way in a computer. There is no decimal point in the binary system so the computer has a method of understanding decimals. This is called floating-point representation.

The decimal point in a real number is called a floating point because it can be placed anywhere - it is not fixed. Because of this, a computer will divide a number into two parts. These are called the mantissa and the exponent.

MantissaEdit

The mantissa is found by taking the real number and removing the decimal point, for example:

1101 . 0111 would become 1101 0111

ExponentEdit

The exponent is the number of spaces the decimal point has moved. In the example above, the decimal point moved 4 places to the left, so the exponent is 0000 0100 (this is binary for 4).

If the decimal point moves to right, the exponent is negative. For example,

0000 . 0111 (mantissa - 0000 0111)
here, the exponent is -1. The binary number for this is 1111 1111 (see Negative binary numbers)

ResultEdit

The result is found by putting the Mantissa and Exponent together. The results for the examples above are:

Decimal Mantissa Exponent Result
1101 . 0111 1101 0111 0000 0100 1101 0111 0000 0100
0000 . 0111 0000 0111 1111 1111 0000 0111 1111 1111

Related pagesEdit