Multiplying Binary Numbers
Multiplying Numbers without Calculators…
Recall that when you first learned to multiply two multi-digit numbers such as \(3124\cdot 425\), you probably used the following procedure:
Step 1: Multiply each digit of the top number by the \(1\)’s digit of the bottom number, keeping the \(1\)’s digit, and carrying the \(10\)’s digit
Step 2: Write a zero below the \(1\)’s digit of what you got in the last step, then repeat step 1, but with the \(10\)’s digit of the second number. Be sure to add the number that got carried in the last step to your answer here.
Step 3: Write a pair of zeros under the \(1\)’s digit and \(10\)’s digit of the last line, and repeat step 1 with the \(100\)’s digit of the second number. Be sure to add any carried numbers to your answer.
Step 4: Add up all three lines to get the final answer.
How Multiplication Works in Base 2
It turns out that multiplication of numbers works exactly the same way in binary, except with the added benefit that you won’t ever need to carry a digit to the next location. In other bases, carrying will be required when the product of the digits you’re multiplying give you a product that is bigger than the base. Perhaps more on this later.
