Binary Addition

The new KS3 National Curriculum for Computing says that students should be able to carry out simple operations on binary numbers, and binary addition is also required for GCSE Computer Science courses.

Luckily the process is exactly the same as when adding normal denary numbers:

  1. align the units columns
  2. start with the right-most column and work right-to-left
  3. if the total of the values in each column requires more than one digit then you need to carry

With denary numbers, if you were adding, say, 6 and 4 then the total would be 10, so we'd write a 0 in that column and carry the 1 and add it into the total for the next column. In binary it's exactly the same, you just need to remember that 1 + 1 = 10, and if you need to include a carried bit then 1 + 1 + 1 = 11.

128
0
64
0
32
0
16
0
8
0
4
0
2
0
1
0
=

0
0
0
0
0
0
0
0
=

Carry:
0
0
0
0
0
0
0

128
0
64
0
32
0
16
0
8
0
4
0
2
0
1
0
= 0


The sum of these values can be represented in eight bits.

You can change the first two numbers either by clicking on the 0s and 1s, or by typing numbers into the boxes. Think of some suitable test cases and what you'd expect the answer to be. What happens if you add two numbers with a total of more than 255?

See how logic circuits can be used to perform additions in the full adder.