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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