Circuit that multiples two numbers together?

Question

Design a combinational circuit that multiplies two numbers together, and outputs the result.

The biggest product will be 3 * 3 = 9. Four bits to represent the product.

0: 00
1: 01
2: 10
3: 11

I need a 4 bit register for the outputs, right?

How do I start my truth table? like this?

A B C D | Output | AB | CD
0 0 0 0   0         0    0

and so onto minterm 15?

How will I form the expressions from the truth table? I know how to solve with a K-map, but I'm having a hard time visualizing and building it.

Answer 1

You seem to be on the right track. You have only 16 possible unique input states, represented as 4 bits. I would start by writing out the truth table containing just the 4 input bits and the 4 output bits. AB and CD may well end up as useful intermediate terms, but don't assume that until you see what the truth table looks like.

Finding sub-expressions and how to combine them to make combinatorial logic implement a particular logic function is exactly what Karnough maps are intended for. Your problem is small enough so that a K-map is tractable.