How many bits will it take to represent a number of this type xxx.xx ?

That is, a number from 000.00 to 999.99

Thanks !!

I have to assume that you want a fixed point representation rather then a floating point one, because your format is xxx.xx and floating point is a very complicated formant.

Because this sounds a lot like a school assignment I'll show you how to solve a simpler version and let you solve the larger one on your own.

xx.x instead of xxx.xx or 00.0 to 99.9

Fixed point means that the number is stored as an integer, but it is assumed that it is always divided by a predetermined number. So if we wanted to save the number 99.9 from above we would assume that we are dividing by 10 and save the number as 999. The next thing we have to figure out is how many bits it would take to encode an integer that has a maximum value of 999 = 99.9 * 10. To do this we need to take the log base 2 of 999 which is 9.96 and round up to 10 because you cannot have part of a bit.

So there is the answer for 00.0 to 99.9, it takes 10 bits. Although in a modern computer you are probably going to need 16 bits because most computers have no way to deal with 10 bit numbers directly.

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