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What is the most efficient way to scale numbers into the range of -1, 1 in Verilog using Cyclone II?
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You do not state the numeric format that you are using.
The conversion of signed fixed-point B-bit integers to fractional integers is conceptual only, so no conversion is required.
For example, a 3-bit signed integer has can represent the integer values -4, -3, -2, -1, 0, 1, 2, 3, with 2's compliment binary representation 100b, 101b, 110b, 111b, 001b, 010b, 011b. In fractional integer format, this is a Q2.0 number.
You can divide this number by 2 to get a Q1.1 representation, i.e., -2.0, -1.5, -1.0, -0.5, 0, 0.5, 1.0, 1.5, or divide by 4 to get a Q0.2 representation, i.e., -1.0, -0.75, -0.50, -0.25, 0.0, 0.25, 0.50, 0.75.
In all cases, the binary representation is the same (ok, there's a slight difference in that you can put a binary-point between the bits, but that does not exist in the hardware implementation).
If you want a B-bit number to represent -1.0 to (almost) 1.0, then you just need to interpret it as a Q0.(B-1) fractional integer format number. It will have the range -1.0 to 1.0-1/(2^(B-1)).
Cheers,
Dave
Honored Contributor
