### A good answer might be:

>      11111 11
>       0000 0110  =   610
>       1111 1010  =  -610
>       ---------    ----
>       0000 0000      010

# Two's Complement

This representation scheme is called two's complement. It is one of many ways to represent negative integers with bit patterns. But it is now the nearly universal way of doing this. Integers are represented in a fixed number of bits. Both positive and negative integers can be represented. When the pattern that represents a positive integer is added to the pattern that represents the negative of that integer (using the "binary addition algorithm"), the result is zero. The carry out of the left column is discarded.

Here is how to figure out which bit-pattern gives zero when added (using the "binary addition algorithm") to a another pattern.

How to Construct the Negative of an Integer in Two's Complement:
Start with an N-bit repn of an integer. To calculate the N-bit repn of the negative integer: Reflect each bit of the bit pattern (change 0 to 1, and 1 to 0). Add one.

An example:

>     The positive integer: 0000 0001   ( one )
>     Reflect each bit:     1111 1110
>     Add one:              1111 1111   ( minus one )

### QUESTION 17:

Fill in the blanks:

>     The positive integer: 0000 0110     ( 610 )

>     Reflect each bit:     ____ ____

>     Add one:              ____ ____     ( -610 )