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K-Map Simplification Guide

The document discusses the Karnaugh Map (K-Map), a tool used for simplifying Boolean expressions to obtain the simplest Sum of Products (SOP) or Product of Sums (POS) expression. It explains the relationship between the number of cells in a K-Map and the number of input variables, providing examples of how to use K-Maps to simplify Boolean expressions. The document includes specific examples demonstrating the mapping and simplification process using K-Maps.

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16 views6 pages

K-Map Simplification Guide

The document discusses the Karnaugh Map (K-Map), a tool used for simplifying Boolean expressions to obtain the simplest Sum of Products (SOP) or Product of Sums (POS) expression. It explains the relationship between the number of cells in a K-Map and the number of input variables, providing examples of how to use K-Maps to simplify Boolean expressions. The document includes specific examples demonstrating the mapping and simplification process using K-Maps.

Uploaded by

hussienyt3
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Islamic University

Computer Technology Engineering


First Class / Digital Electronics

The Karnauph Map

Lec.5

Zaid salami
The Karnaugh Map (K-Map)
 A Karnaugh map provides a systematic method for simplifying Boolean expressions
and, if properly used, will produce the simplest SOP or POS expression possible, known
as the minimum expression.

 The number of cells in a Karnaugh map, as well as the number of rows in a truth
table, is equal to the total number of possible input variable combinations. For three
variables, the number of cells is 23 = 8. For four variables, the number of cells is 24 = 16.
 EXAMPLE : Using the Karnauph Map, find the simplified Boolean expression for the

truth table given below?


 EXAMPLE : Map the following SOP expression on a Karnaugh map:

𝐴 + 𝐴 𝐵 + 𝐴𝐵 𝐶 .

 Solution: 𝐴 + 𝐴 𝐵 + 𝐴𝐵 𝐶

000 100 110

001 101

010

011
 EXAMPLE : Using the Karnauph Map, find the simplified Boolean expression for the
logic expression: 𝐘 =∑ (𝟏,𝟐,𝟑,𝟓,𝟕)

Solution: 𝐘 = 𝑨 𝑩 𝑪 + 𝑨 𝑩 𝑪 + 𝑨 𝑩 𝑪 + 𝑨 𝑩 𝑪 + 𝑨 𝑩 𝑪
001 010 011 101 111
 EXAMPLE : Simplify the following Boolean expression using K-Map:

Y= 𝐀 𝐁 𝐂 𝐃 + 𝐀 𝐁 𝐂 𝐃 + 𝐀 𝐁 𝐂 𝐃 + 𝐀 𝐁 𝐂 𝐃 + 𝐀 𝐁 𝐂 𝐃 + 𝐀 𝐁 𝐂 𝐃 +
𝐀 𝐁 𝐂 𝐃 +𝐀 𝐁 𝐂 𝐃 +𝐀 𝐁 𝐂 𝐃 +𝐀 𝐁 𝐂 𝐃+𝑨 𝑩 𝑪 𝑫

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