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Laumoc, Clark Dave T.

Karnaugh maps (K-maps) are utilized for simplifying Boolean functions, particularly in Product of Sums (POS) form, by organizing zeros to derive minimal expressions. The document provides examples of simplifying both 2-variable and 3-variable Boolean functions using K-maps, detailing the steps to group zeros and formulate the simplified expressions. This technique is essential in digital circuit design to reduce complexity and minimize gate usage.

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Clark Dave Laumoc
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15 views1 page

Laumoc, Clark Dave T.

Karnaugh maps (K-maps) are utilized for simplifying Boolean functions, particularly in Product of Sums (POS) form, by organizing zeros to derive minimal expressions. The document provides examples of simplifying both 2-variable and 3-variable Boolean functions using K-maps, detailing the steps to group zeros and formulate the simplified expressions. This technique is essential in digital circuit design to reduce complexity and minimize gate usage.

Uploaded by

Clark Dave Laumoc
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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Laumoc, Clark Dave T.

BTVTED-ET-3A

Karnaugh maps (K-maps) are widely used for simplifying Boolean functions, including
expressions in the Product of Sums (POS) form. By organizing and grouping zeros (0s) in the K-
map, we can find the minimal POS expression for a function, which can be applied in digital
circuit design to reduce complexity.

Example 1: Simplifying a 2-Variable Boolean Function

Given Boolean function:


F (A, B) = ∏ (0, 1, 2)

Steps:
1. Draw a 2-variable K-map (a 2x2 grid).
2. Mark 0s in the cells corresponding to the minterms 0, 1, and 2.
3. Identify groups of adjacent 0s (forming groups of 1, 2, or 4 cells).
4. Write the simplified POS expression based on the variables in these groups.

Result:
Group the 0s in the map and derive the expression, e.g., (A + B') • (A' + B).

Example 2: Simplifying a 3-Variable Boolean Function

Given Boolean function:


F (A, B, C) = ∏ (1, 2, 4, 5)

Steps:
1. Create a 3-variable K-map (a 2x4 grid).
2. Fill in the K-map with 0s for the minterms 1, 2, 4, and 5.
3. Group the adjacent 0s into the largest possible groups.
4. Convert these groups into the POS expression.

Result:
Identify the groups and simplify, such as (A + B + C')•(A' + B' + C) ….

These examples demonstrate the use of K-maps for finding minimal POS forms, aiding in the
simplification of logic circuits and minimizing gate usage.

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