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Boolean Algebra and Computer Logic
ExErcisEs 8.3
For Exercises 1–8, write the minimal sum-of-products form for the Karnaugh maps of the given figures.
1.
x 1 x 2
x 3
x 1 xЈ 2
xЈ 3
xЈ 1 xЈ 2 xЈ 1 x 2
1
1
1
1
1
2.
x 1 x 2
x 3
x 1 xЈ 2
xЈ 3
xЈ 1 xЈ 2 xЈ 1 x 2
1
1
1
3.
x 1 x 2
x 3
x 1 xЈ 2
xЈ 3
xЈ 1 xЈ 2 xЈ 1 x 2
1
1
1
1
1
1
4.
x 1 x 2
x 3
x 1 xЈ 2
xЈ 3
xЈ 1 xЈ 2 xЈ 1 x 2
1
1
1
5.
x 1 x 2
x 1 x 2
x 1 x 2
x 1 x 2
x 3 x 4
' '
'
'
x 3 x 4 '
x 3 x 4
'
'
x 3 x 4
'
1
1
1
1
1
1
1
1
6.
x 1 x 2
x 1 x 2
x 1 x 2
x 1 x 2
x 3 x 4
' '
'
'
x 3 x 4 '
x 3 x 4
'
'
x 3 x 4
'
1
1
1
1
1
7.
x 1 x 2
x 1 x 2
x 1 x 2
x 1 x 2
x 3 x 4
' '
'
'
x 3 x 4 '
x 3 x 4
'
'
x 3 x 4
'
1
1
1
1
1
8.
x 1 x 2
x 1 x 2
x 1 x 2
x 1 x 2
x 3 x 4
' '
'
'
x 3 x 4 '
x 3 x 4
'
'
x 3 x 4
'
1
1
1
1
1
1
For Exercises 9 and 10, use a Karnaugh map to find the minimal sum-of-products form for the truth functions
shown.
9. x 1 x 2 x 3 f( x 1 , x 2 , x 3 )
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0