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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 22 by 5, which in binary is 10110 by 101:
10110 x 101 (Multiplier)
starting from right to left there is a 1 in the multiplier so we write the number being multiplied normally 10110.
10110 x 101 (Multiplier) ----- 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
10110 x 101 (Multiplier) ------- 10110 1011000 -------
After the number has been multiplied by all the digits in the multiplier we simply add them up using binary addition, be careful when writing the numbers out so they are lined up correctly for addition.
10110 + 1011000 ------- 1101110 -------
Converting 1101110 to denary gives us 110, which is 22x5.