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 significand and the exponent.


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

1101 . 0111 would become 1101 0111


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


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

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

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