Question

Given n is the number of positions in radix-r, how many possibilities are wasted due to the sign position in the signed-magnitude numbering system.

Answer #1

I'm attaching the pic for better understanding:-

As total number possible with n positions =
**r ^{n} (i.e, 0 to r^{n} -1)**

But for signed magnitude one bit will be wasted for sign representation. So, it will not be fully utilized.

For signed-magnitude number possible will be = **2 *
r ^{n-1} (i.e, -r^{n-1} to r^{n-1}
-1)**

So, the numbers wasted will be-

r^{n} - 2 * r^{n-1} = **r ^{n-1} *
(r - 2)**

**If you have any doubt, feel free to ask in comment
section.**

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