Binary Multiplication

Binary multiplication: a reliable method

Binary multiplication works like decimal multiplication, but each digit can only be 0 or 1. The goal is to multiply the binary numbers carefully and write the result in simplest binary form.

1) Multiply digit by digit

Start from the rightmost digit of the bottom number.

• If the digit is 0, the partial result for that row is 0.
• If the digit is 1, copy the top number as that row’s partial result.

2) Shift left for each new place

When you move one place to the left in the bottom number, shift the partial result one position left. In binary, shifting left is the same as adding a zero at the end.

3) Add the partial results

Add all rows using binary addition. Remember that:

• 0 + 0 = 0
• 0 + 1 = 1
• 1 + 1 = 10
• 1 + 1 + 1 = 11

4) Simplify the final answer

Make sure there are no extra leading zeros. The final number should be written in standard binary form.

Quick check

If you want to verify your answer, you can convert both numbers to decimal, multiply them, and compare with the decimal value of your binary result. This is a good way to catch place-value or carry errors.