658
Boolean Algebra and Computer Logic
19. 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
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
20. 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
1
1
1
0
1
0
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
21. a. Find the canonical sum-of-products form for the truth function in the accompanying table.
b. Draw the logic network for the expression of part (a).
c. Use properties of a Boolean algebra to reduce the expression of part (a) to an equivalent expression
whose network requires only two logic elements. Draw the network.
x 1
x 2
x 3
f( x 1 , x 2 , x 3 )
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
22. a. Find the canonical sum-of-products form for the truth function in the accompanying table.
b. Draw the logic network for the expression of part (a).
c. Use properties of a Boolean algebra to reduce the expression of part (a) to an equivalent expression
whose network requires only three logic elements. Draw the network.