31.

a. A(A+B) = A

1

can be derived for each output column from a truth table.

1

1

One output column is taken at a time, and a Boolean product

is written for each output condition that is a 1. After the

b. is

Boolean product which represents each 1 output is written,

the outputs are ORed together to form a MINTERM

EXPRESSION. For example, the diagram below is the truth

table for a circuit that will add two binary digits.

A

B

SUM

CARRY

0

0

0

0

0

1

1

0

1

0

1

0

1

1

0

1

32

To derive a MINTERM EXPRESSION for each output

0

0

0

0

0

1

1

0

column, the Boolean product is written for each 1 output.

1

0

1

0

1

1

0

1

Use only one output column at a time. The Boolean product

for the SUM-output column is derived as follows:

The first 1 occurs when A is 0 and B is 1; thus, the Boolean

product for this condition is AB.

The next 1 occurs when A is 1 and B is 0; thus, the Boolean

product for this condition is AB.