ECE 349 Homework Assignment #3
1. For the function F(a, b, c, d) = Pm(0,1,4,6,7,9,11,13,14) + Pd(2,5,12), list all of
the prime implicants and indicate which of these are essential prime implicants.
2. Use K-maps to find a minimal sum-of-products and a minimal product-of-sums for
f(a, b, c) = Pm(0,1,2,4).
3. Use a K-map to find a minimal sum-of-products for:
f=a0b0+cd0+abc +a0b0cd0+abc0d+a0c0d0.
4. Find two different minimal sum-of-product expressions for:
f(a, b, c, d) = Pm(3,7,11,12,13,15) + Pd(5,8,9,14).
5. Find a minimal product-of-sums expression for the function of Problem 4.
6. Find a minimal product-of-sums expression for:
f(a, b, c, d) = QM(0,2,10,11,12,14,15) ·QD(5,7).
7. Assuming that the inputs abcd = 0101, abcd = 1001, abcd = 1011 never occur, find a
simplified expression for F=a0bc0d+a0b0d+a0cd +abd +abc.
8. A logic network realizes the function F(a, b, c, d) = a0b0+a0cd +ac0d+ab0d0. Assuming
that a=cnever occurs when b=d= 1, find a simplified expression for F.
9. Find the essential prime implicants for:
F(a, b, c, d, e) = Pm(0,3,4,5,6,7,8,12,13,14,16,21,23,24,29,31).
10. Find the minimum sum-of-products expression for:
F(a, b, c, d, e) = Pm(0,2,6,7,8,10,11,12,13,14,16,19,29,30) + Pd(4,9,21).
11. (Optional 2 Points) After completing the design and fabrication of a digital system,
a designer finds that one more inverter is required. However, the only spare gates in
the system are a 3-input OR, a 2-input AND, and a 2-input XOR. How should the
designer realize the inverter function without adding another IC?