Multiplication

Binary Multiplication

Binary Multiplication uses a combination of multiplying by one, shifting and addition. When multiplying a binary number by 10 it is simply shifted to the left into the next column, this multiplies the original number by 2. Multiplying by 100 causes a shift of two places to the left which multiplies the original number by four.

The rules for multiplying a binary number by another binary number is:

For every 1 in the multiplier repeat the number being multiplied with as many zero's to the right of it as there are digits before the 1 in the multiplier.

For every 0 in the multiplier nothing is written.

For example multiply 10110 by 101

starting from right to left there is a 1 in the multiplier so we write the number being multiplied normally 10110.

The second number in the multiplier is a 0 so we write nothing.

The last number in the multiplier is a 1 and there are two digits before it a 0 and a 1, 2 digits, so we write out the number being multiplied with 2 zeros to the right of it, 1011000