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Floating point number normalisation

More on normalisation
Numbers can be represented in different ways using floating-point notation. To illustrate this point using decimal, suppose you have this number: 45379510 How could 45379510 be represented using the floating-point system?

453795 x 102 or 4537 x 104 or 45 x 106 or 0.0045379510 x 1010 and so on.

Look at this example, which uses 10 places after the decimal point: 0.0045379510 x 1010 You could write it like this 0.00453795 x 1010 if you only had 8 places after the decimal point. The problem with this is that you have lost some of the accuracy of the number. (You had to round down the ‘510’ at the end of the number into a ‘5’). If you only had 8 places after the decimal point, you might prefer this: 0.45379510 x 108 You have kept the accuracy and still used only 8 places after the decimal point. Also, by having a smaller number of places after the decimal point, you have increased the number of places you can use for the exponent, thereby increasing the range of numbers you can represent.

How did we keep the accuracy for the same number of mantissa places? We did it by getting rid of 'leading zeros'. In other words, we didn't write down 0.00453 etc, we wrote down 0.453 etc. We ended up with the same number, improved accuracy and still used only 8 places for the mantissa.

The process of ensuring the maximum accuracy for a fixed number of bits is known as ‘normalisation’.

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