Two’s Complement

Two’s complement is the method used by computers to represent integers in binary format. A binary number with an LMb (Left Most bit) of 1 is negative, while a binary number with an LMb of 0 is either a positive number, or 0. The method involves writing out the value in binary format and then inverting the binary value and adding 1.

Example 1:

If we wanted to write out the value of -27 using Two’s Complement, we would do the following:

Firstly, we convert the number to a positive number:

27

We then convert the number to binary:

This gives us:

00011011

We now invert the binary values:

11100100

Lastly, we add 1:

11100101

The above value is a representation of -27 in binary format, note that the LMb is a 1.

Example 2:

If we wanted to convert from a binary number in Two’s Notation back to its negative integer value, we would do the following. Lets use -27 as before.

Firstly, we invert the binary values:

11100101

00011010

We then add 1 to our binary values:

00011011

Lastly, we convert the binary value to an integer:

16 + 8 + 2 + 1 = 27

We convert the integer to a negative because of the LMb, which gives us:

-27