Storing Negative Numbers (Two's Complement)

What you need to Know

Describe and exemplify the use of binary to represent positive and negative integers using two’s complement, including the range of numbers that can be represented using a fixed number of bits.

Sign bits

Negative numbers have a ‘sign bit’ - the first digit of the binary number (closest to the left) is used to show whether the number is positive or negative.

The method for representing negative numbers is called Two’s Complement.

Think Positive - Write out the positive equivalent. For example, if you want to find -89, write out (positive) 89.

Flip the Bits - Switch all the 1s to 0s and the 0s to 1s.

Add 1 - Add 1 to the value of the number. If you’ve got a zero in the last column, write a 1. Otherwise, carry over.

Example 1

Find the number -75:

1. Think Positive - Write out +75

2. Flip the Bits - Flip all the 1s to 0s and the 0s to 1s.

3. Add 1 - Add 1 in the last column.

Example 2

Find the number -28:

1. Think Positive - Write out +28

2. Flip the Bits - Flip all the 1s to 0s and the 0s to 1s.

3. Add 1 - Because it’s an even number, carry over the 1 to the first column that has a 0 and flip the previous 1's to 0's.