Why unsigned fixed point rational has the range 2^a - 2^-b? Where a represents integer bits, and b represents fractional bits of the given number.
How I can determine the max value, unsigned fixed point rational can give?
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The minimum distance representable is defined for the fractional part: 2^-b
The maximum number, will be how much times that minimum distance can be added, that will be 2^nbits-1 times (the amount of numbers that can be represented minus 1 because of 0)
Max range: (2^nbits-1)*2^-b
With some math mangling
nbits=a+b,
(2^nbits-1)*2^-b = 2^(a+b)-1*2^-b=2^a*2^b*2^-b+2^-b=2^a*2^-b
Example:
Q(2,30)
nbits=32
range 0 / 2^2 - 2^-30
minimum distance: 2^-30,
amount of numbers that can be represented: 2^32
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