Integers: 1's complement

Another way to represent negative values:

Negate (flip) each bit.

Use the operator ~ to represent flipping each bit.

~B is B with all of its bits flipped.

This is called 1's complement (1C).

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

B = 01011

-B = 10100

Converting from base 10 to N-bit 1C

1. Ignoring sign, convert value to unsigned N-bit value.

2. If sign is negative, negate (flip) all bits.

1C to base 10

1. If sign bit (msb) is 1, flip all bits.

2. Convert N-bit unsigned value to base 10, using negative value if sign bit was 1.

Range of values

Number of positive values (including +0): 2N-1

Number of negative values (including -0): 2N-1

Total number of different values: 2N - 1