What is the smallest number that can be stored in a 32 bit fixed point system of representation if the radix point is assumed to be in the middle?
My guess would be that 0000000000000000.0000000000000001$_2$ is the smallest number that could be represented which is 0.0000152587890625 in decimal, however I'm not sure if it is correct, as any negative number is smaller than a fraction of a positive number.
I'm a bit confused about how the fixed point system represents negative numbers (2's complement or sign magnitude) and if that would affect the smallest number that can be represented by the 32 bit fixed point system.
Best Answer
That seems to be the smallest non-zero number.
Of course, $0$ is smaller, but that's self-evident.
Usually we say that something like $-1,234,567,890$ is a large negative number rather than a small number. Something like $-0.000000001$ is small and negative, while $0.000000001$ is small and positive.
All of that to say I think you've met the intent of the question. The "radix in the middle" tells you how many bits are allocated to each side of the decimal. As to "two's complement" and the like, those don't really affect the precision of what you store in the number.