# Finding bias with n-bit number representations given max and min

I'm a bit stuck on this question (not sure if it comes under math but if it doesn't please help me find which topic to put it in) :

If you want an n bit number to have a max value of x (positive) and min value of -(x-1) which is negative, what would the bias be? Note -- the bias is negative, meaning for example, if a number was 0000 and the bias was 8, then the number would end up being 0000-8 = -8.

Here's what I'm thinking so far -- for an n-bit number representation, the range is $$[-2^{n-1}, 2^{n-1}-1]$$.

Since this is biased, we want: $$2^{n-1}-1-bias = x$$ and $$-2^{n-1}-bias = -(x-1)$$

but when I try to solve for bias I get that bias is 1, because almost everything cancels out. but it isn't the right answer. Would love some advice and suggestions

• I'll have a look at this one too, Melanie. I've only semi-understood your question, though, primarily because I have not understood what the "bias" is. If you can give me a reference, like a video or a book or a paper which explains it, I can look it up and get back to you on this one. Jan 28, 2021 at 9:06