Homework 2

Max marks: 110

Row x1 x2 x3 f

0 0 0 0 0

1 0 0 1 1

2 0 1 0 1

3 0 1 1 0

4 1 0 0 1

5 1 0 1 0

6 1 1 0 0

7 1 1 1 1

Table 1: Truth table for a 3-way light switch

1 Sept 10th Lecture

Problem 1 If the SOP form for ¯f = AB¯C¯ +

A¯B¯, then give the POS form for f. [10 marks]

Problem 2 Use DeMorgan’s Theorem to find f

if ¯f = (A + BC)D + EF. [10 marks]

Problem 3 Implement the function in Table 1

using only NAND gates. [10 marks]

Problem 4 Implement the function in Table 1

using only NOR gates. [10 marks]

2 Sept 13th Lecture

Problem 5 Find the minimum-cost SOP and

POS forms for the function f(x1, x2, x3) =

m(1, 2, 3, 5). [1, Prob 2.37] [10 marks]

Problem 6 Find the minimum-cost SOP and

P

POS forms for the function f(x1, x2, x3) =

m(1, 4, 7) + D(2, 5). [1, Prob 2.38] [10 marks]

Problem 7 Find the minimum-cost SOP and

Q

POS forms for the function f(x1, x2, x3, x4) =

M(0, 1, 2, 4, 5, 7, 8, 9, 10, 12, 14, 15). [1, Prob

2.39] [10 marks]

Problem 8 Find the minimum-cost SOP and

POS forms for the function

P

f(x1, x2, x3, x4) =

m(0, 2, 8, 9, 12, 15) + D(1, 3, 6, 7). [1, Prob

2.40] [10 marks]

Problem 9 Derive a minimum-cost realization

of the four-variable function that is equal to 1 if

exactly two or exactly three of its variables are

equal to 1; otherwise it is equal to 0. [1, Prob

2.46] [10 marks]

Problem 10 Find the minimum-cost SOP and

POS forms for the function

P

f(x1, . . . , x5) =

m(0, 1, 3, 4, 6, 8, 9, 11, 13, 14, 16, 19, 20, 21, 22, 24, 25)+

D(5, 7, 12, 15, 17, 23). [1, Prob 2.42] [10 marks]

References

[1] S. Brown and Z. Vranesic. Fundamentals of

Digital Logic with Verilog Design: Third Edition. McGraw-Hill Higher Education, 2013.

1