**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 10 ^{2} or 4537 x 10^{4} or 45 x 10^{6} or 0.0045379510 x 10^{10} and so on.**

Look at this example, which uses 10 places after the decimal point: 0.0045379510 x 10^{10} You could write it like this 0.00453795 x 10^{10} 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 10^{8} 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’.