I was given a review homework assignment recently for my Embedded Systems class. Most of it was just basic things such as converting decimal numbers to binary and hex and the sort, however I came across a problem on minimizing an expression to sum-of-products (SoP) form where the function yielded a summation of a bunch of values. It certainly didn’t help that I’ve been out of school for a bit, and most of what I was finding online to help me figure this out was on reducing a boolean function to sum-of-products form instead. Now that I’ve solved the problem, I figured I’d be a model citizen of the internet and post on how to come up with a solution for the problem to save some wasted time and effort for others.

Let’s say you are given the expression,

To solve this you would go through 4 simple steps:

1. Change each of the numbers in the summation into binary
2. Map the binary numbers into a Karnaugh Map
3. Group the Karnaugh Map as necessary
4. Interpret the expression.

Change each of the numbers in the summation into binary. In order, this would give you:

0000, 0001, 0010, 0011, 0100, 0101, 0110, 1010, 1011

Map the binary numbers into a Karnaugh Map.

Group the Karnaugh Map as necessary.

Interpret the expression. Thus, the reduced boolean expression in sum-of-products form is