682
Boolean Algebra and Computer Logic
In Exercises 25–28, use the Quine–McCluskey procedure to find the minimal sum-of-products form for the
Boolean expressions.
25. x 1 x 2 ′x 3 x 4 ′ + x 1 ′x 2 ′x 3 x 4 + x 1 ′x 2 x 3 x 4 + x 1 ′x 2 ′x 3 ′x 4 ′ + x 1 ′x 2 x 3 ′x 4 ′ + x 1 ′x 2 ′x 3 ′x 4
26. x 1 x 2 x 3 x 4 + x 1 x 2 ′x 3 x 4 + x 1 x 2 x 3 x 4 ′ + x 1 x 2 ′x 3 x 4 ′ + x 1 ′x 2 x 3 x 4 ′ +
x 1 x 2 x 3 ′x 4 ′ + x 1 ′x 2 x 3 ′x 4 ′ + x 1 x 2 x 3 ′x 4 + x 1 ′x 2 x 3 ′x 4
27. x 1 x 2 x 3 x 4 + x 1 x 2 x 3 x 4 ′ + x 1 ′x 2 x 3 x 4 ′ + x 1 x 2 x 3 ′x 4 ′ + x 1 ′x 2 ′x 3 ′x 4 ′ +
x 1 ′x 2 x 3 ′x 4 ′ + x 1 x 2 ′x 3 ′x 4 + x 1 ′x 2 ′x 3 ′x 4 + x 1 x 2 x 3 ′x 4
28. x 1 ′x 2 x 3 ′x 4 x 5 ′ + x 1 ′x 2 x 3 x 4 ′x 5 + x 1 x 2 x 3 x 4 x 5 + x 1 ′x 2 ′x 3 x 4 ′x 5 +
x 1 x 2 ′x 3 x 4 x 5 + x 1 ′x 2 ′x 3 ′x 4 ′x 5 + x 1 x 2 ′x 3 x 4 ′x 5 + x 1 x 2 x 3 x 4 ′x 5 ′ +
x 1 x 2 x 3 ′x 4 x 5 + x 1 ′x 2 ′x 3 ′x 4 x 5 ′
29. Use the Quine–McCluskey procedure to find a minimal sum-of-products form for the truth function
illustrated by the map in Figure 8.34.
For Exercises 23 and 24, use the Quine–McCluskey procedure to find the minimal sum-of-products form for
the truth functions in the given tables.
23. x 1
x 2
x 3
x 4
f( x 1 , x 2 , x 3 , x 4 )
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
24. x 1
x 2
x 3
x 4
f( x 1 , x 2 , x 3 , x 4 )
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1