Seven bit and two compliment

If we use seven-bit two's complement binary representation for integers, what is The number of integers (things) that can be represented in this way? The smallest (most) negative integer that can be represented in this way? The largest positive integer that can be represented in this way?

This is a CS homework question that I am having trouble answering and explaining. Any help would be appreciated.

Solution

So its really easy

Counting in binary usually goes like

>00000000 (8) = 0
>00000001 (8) = 1
>00000010 (8) = 2
>00000011 (8) = 3
>etc...etc.

In 7 bit the last bit is what decides if its a negative or positive

1 being negative and 0 being positive

> 10000000 = -128
> 10000001 = -127
> 10000010 = -126
> On...and on...
> 11111111 = -1
> 00000000 = 0
> 00000001 = 1
> 01111111 = 127

So lowest you can go is -128

Highest you can go is 127