SIMON FRASER UNIVERSITY
School of Mechatronic Systems Engineering
MSE 352 Digital Logic and Microcontrollers
Problem Set 3
1- For the Boolean Function 𝐹𝐹, as given in the following truth table:
𝑋𝑋
0
0
0
0
1
1
1
1
𝑌𝑌
0
0
1
1
0
0
1
1
𝑍𝑍
0
1
0
1
0
1
0
1
𝐹𝐹
1
1
0
1
0
1
0
1
(a) List the minterms associated with of F
(b) Express 𝐹𝐹 in sum-of-minterms algebraic form
(c) Express 𝐹𝐹 in product-of-maxterms algebraic form
2- Obtain the truth table of the following functions, and express each function in sum-ofminterms and product-of-maxterms form:
(a) x´z´+ y´z´+ yz´ + xy
(b) ACD´ + C´ D + AB´ + ABCD
3- Optimize the following Boolean functions by means of Karnaugh map:
(a) F (A, B, C, D) = ∑ (4, 6, 7, 15)
(b) F (A, B, C, D) = ∑ (3, 7, 11, 13, 14, 15)
(c) (w, x, y, z) = ∑ (2, 3, 12, 13, 14, 15)
4- Simplify the following Boolean expressions, using three-variable maps:
(a) xy + x´y´z´ + x´yz´
(b) x´y´+ yz + x´yz´
(c) F(x, y, z) = x´y + yz´ + y´z´