Higher Engineering Mathematics

BOOLEAN ALGEBRA AND LOGIC CIRCUITS 109

A

Figure 11.27

Now try the following exercise.

Exercise 50 Further problems on logic

circuits

In Problems 1 to 4, devise logic systems to meet

the requirements of the Boolean expressions

given.

1.Z=A+B·C

[See Fig. 11.28(a)]

2.Z=A·B+B·C

[See Fig. 11.28(b)]

3.Z=A·B·C+A·B·C

[See Fig. 11.28(c)]

4.Z=(A+B)·(C+D)

[See Fig. 11.28(d)]

Figure 11.28

Figure 11.28 Continued

In Problems 5 to 7, simplify the expression given

in the truth table and devise a logic circuit to meet

the requirements stated.

5. Column 4 of Table 11.20
   [Z 1 =A·B+C, see Fig. 11.29(a)]


6. Column 5 of Table 11.20
   [Z 2 =A·B+B·C, see Fig. 11.29(b)]

Table 11.20

1 2 3 4 5 6

A B C Z 1 Z 2 Z 3

0 0 0 0 0 0

0 0 1 1 0 0

0 1 0 0 0 1

0 1 1 1 1 1

1 0 0 0 1 0

1 0 1 1 1 1

1 1 0 1 0 1

1 1 1 1 1 1

Figure 11.29