EE-18
Assignment #2

Be sure to show all of your work for each problem.

1. Using DeMorgan's theorem, express the function

        F = X'Y' + Y'Z + XY
a) with only OR and complement operators.
b) with only AND and complement operators.

2. Find the truth tables for the following functions and write each function in its sum-of-minterm form and a product-of-maxterm form. Write each maxterm and minterm out, do not use the shorthand notation.

a. F = (A'+B)(B'+C)
b. G = A'B + ABC' + BC

3. For the Boolean functions F and G, as given in the following truth table:
 
A
B
C
F
G
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
a) List the minterms and maxterms of each function.
b) List the minterms and maxterms of F' and G'.
c) List the minterms of F+G and FG.
d) Express F and G in shorthand sum-of-minterms form.
e) Simplify F and G to expressions with a minimum number of literals.

4. Find all the prime implicants for the following Boolean expressions and determine which are essential.

a) F(A,B,C,D) = Sm(0,2,3,5,7,8,10,11,14,15)
b) F(W,X,Y,Z) = Sm(1,3,4,5,9,10,11,12,13,14,15)

5. Simplify the following functions by means of a 3-variable Kmap to a sum of product form.

a) F = A'C' + BC' + ABC
b) G = X'Y + Y'Z + X'Y'Z'
c) H = A'B' + B'C + AC' + A'BC'

6. Simplify the following functions by using a 4-variable Kmap to a sum of product form.

a) F(W,X,Y,Z) = Sm(1,3,9,11,12,13,14,15)
b) F(A,B,C,D) = Sm(1,2,4,6,7,13,15)
c) F(W,X,Y,Z) = Sm(0,1,2,5,8,10,11,13)
d) F(W,X,Y,Z) = Sm(0,2,4,5,6,7,8,10,13,15)

7. Use a Kmap to simplify the following expressions to a product of sums form.

a) F = ABCD + A'CD + B'D + AC'
b) F = (B+C'+D')(A'+B+D')(A+B'+C')(A'+B'+D')

8. Simplify the following Boolean functions, F, together with the don't-care conditions, d, in sum-of-products form.

a) F(W,X,Y,Z) = Sm(0,2,4,5,8,14,15), d(W,X,Y,Z) = Sm(7,10,13)
b) F(A,B,C,D) = Sm(4,6,7,8,12,15), d(A,B,C,D) = Sm(2,3,5,10,11,14)

 

9.  Simplify the following expression and implement only with NAND gates. You may assume all variables and their complements are available.

F = AB' + ABD + A'B'D' + A'BC' + ABD'

10. Simplify the following expression and implement only with NOR gates. You may assume all variables and their complements are available.

F = W'YZ' + YZ' + WX'

11. Prove that the dual of the exclusive-OR is also its complement.