Minterms & Maxterms in Karnaugh Maps: Clear Notation & Practical Examples

This section clarifies the notation commonly used to list minterms and maxterms in Karnaugh maps. It offers no new theory but provides a concise, practical reference.

Terminology for Minterms

The Greek letter Σ (sigma) denotes a sum, and the lowercase “m” specifies minterms. Together, Σ m means “sum of minterms.” The following example illustrates the format.

f(A,B,C,D) = Σ m(1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 15)
or
f(A,B,C,D) = Σ(m1,m2,m3,m4,m5,m7,m8,m9,m11,m12,m13,m15)

The numbers correspond to cell addresses on the Karnaugh map shown below. This compact notation efficiently lists the minterms (1s) in a K‑map.

Once the minterms are identified, they can be grouped in the usual way to derive a Sum‑of‑Products expression.

Terminology for Maxterms

For maxterms, the Greek letter Π (pi) represents a product, and the uppercase “M” denotes maxterms. Thus, Π M means “product of maxterms.” The same example demonstrates this notation.

f(A,B,C,D) = Π M(2, 6, 8, 9, 10, 11, 14)
or
f(A,B,C,D) = Π(M2, M6, M8, M9, M10, M11, M14)

Here, the numbers refer to the K‑map cells containing zeros. Grouping these cells yields a Product‑of‑Sums solution.

$$Out = (A + B + ar{C} + D)(A + ar{B} + ar{C} + D) + (ar{A} + B + C + ar{D}) + (ar{A} + B + ar{C} + D)$$ $$(ar{A} + B + ar{C} +ar{D})(ar{A} + ar{B} + ar{C} + D)$$

RELATED WORKSHEETS:

• Sum-of-Products and Product-of-Sums Expressions Worksheet
• Karnaugh Mapping Worksheet
• Boolean Algebra Worksheet