Multiplication

As promised, we have a bonus section for you about binary multiplication. Just like binary addition, let's start with a single bit.

a	b	a * b
0	0	0 * 0 = 0
0	1	0 * 1 = 0
1	0	1 * 0 = 0
1	1	1 * 1 = 1

Binary multiplication works the same way as decimal multiplication. If one of the numbers is 0, the product is 0. Only if both numbers are 1 is the product 1. Hopefully, you noticed the truth table right away. It's just the same as the truth table of the and gate. So 1-bit multiplication is really just 1-bit and.

2-bit Multiplication

Let's first look at a sample 2-bit multiplication with 10 x 11:

sample 2-bit multiplication with numbers

This works exactly the same as decimal multiplication. Now, instead of using concrete numbers, let's generalize this process using variable for each digit. So we will be multiplying two 2-bit numbers a and b. Since they are both 2 bits, we can express the digits of a as a1 a0 and the digits of b as b1 b0. The process is exactly the same as the previous number example:

sample 2-bit multiplication with variables

Now it's your turn to implement the 2-bit multiplier in Sim.

Here's the header:

mul2 a[2] b[2] -> [4]

Notice that the output size is 4 because the result of multiplying two 2-bit numbers can fill up 4 digits:

    11
x   11
――――――
    11
+  11
――――――
  1001

Hints

If you get stuck, click on "See Hints".

See Hints

Do you recall a circuit we built for adding two 1-bit number? Also try breaking the problem down into three stages.