Integers: 2's complement

2's complement (2C) may not be intuitively obvious, but it has nice properties

Negation

1. flip all bits

2. add 1 (ignoring any carry out of the msb)

Example: 11ten is 01011 in 5-bit unsigned binary.  Call this number B.

1. flip bits:

10100

~B

2. add 1:

+       1

10101

-B

What do we get if we add this to the original number?

01011

B

+

10101

+    -B

00000

0

If we negate B (-B) using 2C and negate again (--B) we get the original value B back.

1. flip bits:

01010

~(-B)

2. add 1:

+       1

01011

B

Other ways to do N-bit 2C negation:

1. Find the rightmost 1 bit, then flip all the higher bits (bits to the left).

Example:

01011

Rightmost 1 bit is b0

flip bits to the left:

10101