I'm a little lost on this. I need to use two fractional bits
0.(a-1)(a-2)
Like that, now I can use .00 .01 .10 and .11
But I need negative numbers (in 2's complement) also, so would .10 be -.5 ? or would it be -.25 ?
The same with .11 , that would be -.75? or would it be -.5 ?
I'm pretty sure it would be the former in both cases, but I'm not entirely positive.
In two's complement notation, all of the most significant bits of a negative number are set to 1. Let's assume you're storing these numbers as 8 bits, with 2 to the right of the "binary point."
By definition, x + -x = 0, so we can write:
0.5 + -0.5 = 0.10 + 111111.10 = 0 // -0.5 = 111111.10
0.25 + -0.25 = 0.01 + 111111.11 = 0 // -0.25 = 111111.11
0.75 + -0.75 = 0.11 + 111111.01 = 0 // -0.75 = 111111.01
and so on.
Using 8 bits like this, the largest number you can store is
011111.11 = 31.75
the least-positive number is
000000.01 = 0.25
the least-negative number is
111111.11 = -0.25
and the smallest (that is, the most negative) is
100000.00 = -32