Question
Asked Sep 16, 2019
  1. Using the following truth table, write the equivalent Boolean equations in Sum of Product and Product of Sum forms

x

y

z

F

0

0

0

1

0

0

1

0

0

1

0

0

0

1

1

1

1

0

0

0

1

0

1

0

1

1

0

1

1

1

1

0




check_circleExpert Solution
Step 1

Simplification of Sum Of Products (SOP):

The truth table of the SOP is as follows

0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
1
1
C
1
1
1
1
0
N
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0 0 0 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 0 1 1 0 0 1 1 C 1 1 1 1 0 N

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Step 2

The min terms for the given values is as follows.

Min terms
X
mo =xy'z
0
0
0
m-xy'z
0
0
1
1
m2 x'yz'
0
C
m3=x'yz
0
1
1
m4=xy'2
1
C
0
1
0
1
mg=xyz
m6=xyz
1
1
C
1
1
1
m,=xyz
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Min terms X mo =xy'z 0 0 0 m-xy'z 0 0 1 1 m2 x'yz' 0 C m3=x'yz 0 1 1 m4=xy'2 1 C 0 1 0 1 mg=xyz m6=xyz 1 1 C 1 1 1 m,=xyz

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Step 3

The SOP form can be written as F=∑(m0+m4+m6)

By expanding the above equation, we get, F= m0+m4+m6

By substituting the respective min terms in the above equation, ...

F x'y'z'xy'z'+xyz
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F x'y'z'xy'z'+xyz

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Tagged in

Engineering

Computer Science

Boolean Logic

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