range of values for fixed point numbering

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hello all,
I understand this is a very basic doubt to post. but please help me out in this. My problem is, It has been said floating point numbers give a wider range of values compared to fixed point representations. I came to know the range of values for double precision floating point numbers are from -10^308 to 10^308. What is the similar range of values in fixed point?
 

As far I know, no similar precision such as that can be achievable at another representations than float point.


+++
 
Floating point numbers have a higher precision owing to the way they are represented. They have a sign bit, an 8 bit exponent and a 23 bit value. It is the exponent which gives the flexibility in floating point numbers. Have a look at IEEE 754 format for more details.

In fixed point numbers, the number of values after the decimal is fixed. They are represented in something called the Q format. E.g. Q15 format has the MSB as sign bit and the remaining 15 bits are used to represent the values after the decimal. There is no exponent in this fixed point format. Hence, the range of numbers is limited. There are various such Q formats which you can choose based on your design. So the range of values varies based on the specific format you choose.
 
With N bits, you can represent 2^N equally spaced numbers in fixed point.
Which are those numbers is a matter of the numbering system or representation, for example:

* Positive integers from 0 to 2^N-1 in unsigned integer format
* Integers From -2^(N-1) to -2^N-1 in signed integer format
* fractional numbers from -1 to +1-1/(2^(N-1)) with step [1/(2^(N-1))] in fractional format
...etc...

Z
 
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