The following questions are practice problems associated with the lecture material on the subject of Boolean Algebra. These "bigger problems" have appeared on past exams in this course; variation of them will be found on your first exam in a few weeks. Is best to solve these algebracic derivations with paper and pencil, rather than by guessing and pushing buttons, by the way! (Go back to homepage.)

1. Which of the following relationships represents the dual of the Boolean property x + x' = 1? (Note: * = AND, + = OR)
   1. x'* x = 1
   2. x * x'= 1
   3. x + x'= 0
   4. x * x'= 0
   5. x'* x = 0

2. An equivalent representation for the Boolean expression A' + 1 is
   1. A
   2. A'
   3. 1
   4. 0

3. Simplification of the Boolean expression (A+B+C)(D+E)' + (A+B+C)(D+E) yields which of the following results?
   1. A + B + C
   2. D + E
   3. A'B'C'
   4. D'E'
   5. None of the above

4. Given the function F(A,B,X,Y) = AB + X'Y, the most simplified Boolean representation for F' is
   1. (AB)' + (X'Y)
   2. A'B' + XY'
   3. (A'+ B')(X + Y')
   4. (AB + X'Y)'
   5. (AB)'(X'Y)'

5. An equivalent representation for the Boolean expression A + A' is
   1. 1
   2. 0
   3. A
   4. A'
   5. A'*A

6. Simplification of the Boolean expression AB + ABC + ABCD + ABCDE + ABCDEF yields which of the following results?
   1. ABCDEF
   2. AB
   3. AB + CD + EF
   4. A + B + C + D + E + F
   5. A + B(C+D(E+F))

7. Given the function F(X,Y,Z) = XZ + Z(X'+ XY), the equivalent, most simplified Boolean representation for F is
   1. Z + YZ
   2. Z + XYZ
   3. XZ
   4. X + YZ
   5. none of the above

8. Given that F = A'B'+ C'+ D'+ E', which of the following represent the correct expression for F'?
   1. F'= A+B+C+D+E
   2. F'= ABCDE
   3. F'= AB(C+D+E)
   4. F'= AB+C'+D'+E'
   5. F'= (A+B)CDE

9. Simplification of the Boolean expression (A+B+C) + (A+B+C)'(D+E) yields which of the following results?
   1. A + B + C
   2. D + E
   3. A'B'C'
   4. D'E'
   5. A+B+C+D+E

10. Which of the following Boolean functions is algebraically complete?
    1. F = xy
    2. F = x + y
    3. F = x'
    4. F = xy + yz
    5. F = x + y'

11. Which of the following relationships represents the dual of the Boolean property x + x'y = x + y Choose the best answer.
    1. x'(x + y') = x'y'
    2. x(x'y) = xy
    3. x*x' + y = xy
    4. x'(xy') = x'y'
    5. x(x' + y) = xy

12. Simplification of the Boolean expression (A + B)'(C + D + E)' + (A + B)' yields which of the following results?
    1. A + B
    2. A'B'
    3. C + D + E
    4. C'D'E'
    5. A"B'C'D'E'

13. Given that F = (A + B'+ C)(D + E), which of the following represents the only correct expression for F'?
    1. F' = A'BC'+ D'+ E'
    2. F' = AB'C + DE
    3. F' = (A'+ B + C')(D'+ E')
    4. F' = A'BC' + D'E'
    5. F' = (A + B'+ C)(D'+ E')

14. Simplification of the Boolean expression AB + A(BC)' yields which of following results?
    1. A
    2. BC
    3. B
    4. AB
    5. (BC)'

15. Simplifing (AB)' + A'B to most basic form yields which of the following expressions?
    1. A'
    2. B'
    3. A+B
    4. B
    5. (AB)'

16. Which of the following Boolean functions is not algebraically complete?
    1. (xy)'
    2. (x+y)'
    3. xy + yz
    4. xy + yz'
    5. x'+ y'