29.

31. The truth table provides a simple means for testing the

a. 23=8

logical equivalence of two or more Boolean expressions. To

test the logical equivalence of two expressions, construct a

b. 2 =4

2

truth table for both expressions. If both expressions have the

c. 23 = 8

same truth value for each case (row) in the truth table, the

expressions are equivalent and can be substituted for each

d. 22 = 4

other. For example: Prove that A+AB=A.

e. 24 =16

0

0

0

0

1

0

1

0

0

1

1

0

0

1

1

1

1

1

1

1

The third column in the truth table above represents the

30

logical product (AB) for two variables. The fourth column

represents the logical product and sum (A+AB) of two

C

D SUM CARRY

0

0

0

0

variables. A "1" is placed in this column when either the A

0

1

1

0

1

0

1

0

column or the AB column or both have a truth value of 1.

1

1

0

1

The fifth column is a comparison of the first column (A) and

the fourth column (A+AB). A 1 is placed in this column

whenever the truth value of the two columns is the same;

i.e., both 0 or both 1.

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