### A good answer might be:

>            128  =  1000 0000

>        reflect  =  0111 1111

>        add one  =  1000 0000   ??????

# Range of Integers with 2's Complement

Range of N Bit 2's Complement
    -(2(n-1))  ... 0 ... 2(n-1) - 1
    eg n= 8

    -(2(8-1)) = -128  ... 0 ... 2(8-1) - 1 = 127

This is not good. A non-zero integer and its negative can't both be represented by the same pattern. So +128 can not be repd in eight bits. The maximum positive integer that can be repd in eight bits is 12710. The negative integers -1 .. -12710 also can be represented.

What number is represented by 1000 0000? Add the repn of 12710 to it:

>        1000 0000    = ?
>        0111 1111    = 12710
>        ---------
>        1111 1111    =  -110

A good choice for ? is -12810. Therefore 1000 0000 represents -12810. Eight bits can represent the numbers -12810 ... 0 ... +12710.

### QUESTION 20:

How many integers are there in the range -12810 ... 0 ... +12710.

How bit patterns can be formed with 8 bits?