Simplifying Karnaugh Maps by Making Groups of a Non-Power-of-Two Number of Elements

Abstract

When we study the Karnaugh map in the switching theory course, we learn that the ones in the map must be combined in groups of $a \times b$ elements, being $a$ and $b$ powers of two. The result is the logic function described as a sum of products. This paper shows that we can also make groups where $a$ and/or $b$ are equal to three. This does not result in a sum of products, but in a logic function that is simpler than the sum of products in terms of logic gates. This idea is extended later in the paper to groups of $2^n-1$ elements.