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Computing Academy GCSE Computer Science

Binary Addition When

Binary Addition When using the decimal system to add two numbers together such as 26 plus 36 we would do: Tens Units 2 6 + 3 6 1. To add these two numbers, we first consider the ‘units’ column and calculate 6 plus 6, which results in 12. 2. Since 12 is greater than 9 (remembering that base 10 operates with digits 0-9), we ‘carry’ the 1 from the ‘units’ column to the ‘tens’ column and leave the 2 in the ‘units’ column. Tens Units 2 6 + 3 6 1 2 3. Considering the "tens" column, we calculate 1 + (2 + 3), which results in 6. Since 6 is less than 9, there is nothing to "carry" and we leave 6 in the "tens" column. Tens Units 2 6 + 3 6 6 2 Binary addition works in the same way, except that only 0's and 1's can be used. This actually makes binary addition much simpler than decimal addition. Here’s an example. 63

8 4 2 1 0 1 0 1 + 0 1 1 1 1. To add these two numbers, we first consider the ‘1’ column and calculate 1 + 1 which equals 2. In binary ‘2’ is written as 10. We carry the 1 to the ‘2’ column and leave the 0 in the ‘1’ column. 8 4 2 1 0 1 0 1 + 0 1 1 1 1 0 2. Moving on to the ‘2’ column, we calculate 1 + (0 + 1), which again in binary is 10. We carry the 1 to the ‘4’ column and leave the 0 in the ‘2’ column. 8 4 2 1 0 1 0 1 + 0 1 1 1 1 0 0 3. We now look at the ‘4’ column and calculate 1 + (1 + 1). This equals 3 which in binary is written as 11. We carry 1 to the ‘8’ column and leave 1 in the ‘4’ column. 8 4 2 1 0 1 0 1 + 0 1 1 1 1 1 0 0 64

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