Binary Addition

Binary addition basics

Binary uses only 0 and 1. When adding, work from the rightmost digit to the left, just like decimal addition, but remember the only carry that can happen is 1.

1) Know the simple sums

• 0 + 0 = 0
• 0 + 1 = 1
• 1 + 1 = 10 → write 0, carry 1
• 1 + 1 + 1 = 11 → write 1, carry 1

2) Add column by column

Start at the far right.

• Add the two bits in that column.
• If there is a carry from the previous column, include it.
• Write the result bit under the column.
• Carry to the next column only when the sum is 2 or 3.

3) Continue through all digits

Keep moving left until every column is handled. If a carry remains after the leftmost column, place it at the front of the answer.

4) Check your work

A good check is to convert the numbers to decimal, add them, and then compare with the binary result. You can also re-add the columns to make sure each carry was handled correctly.

Example pattern

For a column with a carry-in:

• 1 + 0 + 1 = 10
• 1 + 1 + 1 = 11

Careful carrying and neat alignment are the keys to a correct simplified answer.