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Karnaugh-Map

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Designing Combinational Logic

Circuits

Step 1: Interpret the problem and set up a truth table

o escr e s opera on.

Step 2: Write the product term for each case where

the output is 1. Step 3: Write the SOP expression for the output.

Step 4: Simplify the output expression if possible.

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ep : mp e men e c r cu or e s m p e

expression.

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Design Example 1:

Design a logic circuit that has3 i n uts A B a nd C whose  ,output will be HIGH onlywhen a majority of theinputs are HIGH.

Step 1: Understand theproblem and set up the truthtable.

The output X should be 1

 A B C X

0 0 0 0

0 0 1 0

0 1 0 0

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whenever two or moreinputs are 1. For othercases, the output is 0.

 

1 0 0 0

1 0 1 1

1 1 0 1

1 1 1 1

Design Example 1 (continued)

Step 2: Write the  A B C X

pro uc erm o e ac

case where the output

is 1.

Step 3: Write the SOP

expression for the

output.

 

0 0 1 0

0 1 0 0

0 1 1 1

1 0 0 0

1 0 1 1 A’BC

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x=A’BC+AB’C+ABC’+ABC

 

1 1 0 1

1 1 1 1

 AB’C

 ABC’

 ABC

Design Example 1 (continued)

Step 4: Simplify the output expression

0 0 0 1BC

A

0

1

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0   0

110

1

1

0

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X=AC+BC+AB