Quiz2-solution.docx

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nd

2 Quiz - Solution

Part 1. Theoretical. Choose the best letter of the correct answer. (2 points each)

Ans. D. all of the above Part 2. Calculation (5 points each)

1.

Convert the following SOP expression to an equivalent POS expression.





F  A B C  B D   B B C a.

 A  B  C  A  B  C  A  B  C 

b.

 A  B  C   A  B  C  A  B  C 

c.

 A  B  C  A  B  C  A  B  C 

d.

 A  B  C   A  B  C  A  B  C 

Ans. BONUS 2.

The commutative law of Boolean addition states that A + B = A × B a. True b. False

Ans. B. False 3.

For the SOP expression ABC  ABC  ABC how many 1s are in the truth table's output column? a. 1 b. 2 c. 3 d. 5

Ans. C. 3 4.

Simplify the following Boolean expressions to a minimum number of literals. 6. A 0 0 0 0 1 1 1 1

F  A ' B ' C ' A ' BC ' A ' BC  ABC ' ABC F  A ' B ' C ' A ' B (C' C )  AB(C' C ) F  A'B'C' A'B AB F  A'B'C' B(A' A) F  A ' B ' C ' B F  A ' C ' B

A



B C  B D   A B C

solution :  ( AB 'C AB'BD A'B') C  (AB'C A'B') C  AB'CC A ' B ' C  AB ' C  A ' B ' C

 2n

 B ' C ( A  A ')

2

 B 'C

8

Given the function

Ans. D. 8 5.

What is the primary motivation for using Boolean algebra to simplify logic expressions? a. It may make it easier to understand the overall function of the circuit. b. It may reduce the number of gates. c. It may reduce the number of inputs required. d. all of the above.

Output 1 0 1 1 0 0 1 1

F   m(0, 2,3, 6, 7)

solution : 3

C 0 1 0 1 0 1 0 1

solution :

7. A truth table for the SOP expression ABC  ABC  ABC has how many input combinations? a. 1 b. 2 c. 4 d. 8

B 0 0 1 1 0 0 1 1

8.

F  xy  xy ' y ' z

Give the minterm list form and maxterm list form of the function F.

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solution : min term, F  xy  z  z '  xy '  z  z '  y ' z  x  x ' 

G   A ' BC  A ' D  '

F  xyz  xyz ' xy ' z  xy ' z ' xy ' z  x ' y ' z F  m7  m6  m5  m4  m5  m1

G   A ' BC  A  D ' G  A ' A  A ' D ' ABC  BCD '

F   m 1, 4,5, 6, 7 

G  A ' D ' ABC  BCD ' G  ABC  A ' D '

max term, F   M  0, 2,3 9.

13. A burglar alarm is designed so that it senses four input signal lines. Line A is from the secret control switch, line B is from a pressure sensor under a steel safe in a locked closet, line C is from a battery-powered clock, and line D is connected to a switch on the locked closet door. The following conditions produce a logic 1 voltage on each line.

Construct the truth table.

Solution: x 0 0 0 0 1 1 1 1

y 0 0 1 1 0 0 1 1

z 0 1 0 1 0 1 0 1

f 0 1 0 0 1 1 1 1

Part 3. Designing. Obtain the simplified Boolean expressions for output F and G in terms of the input variables in the circuit of figure below. 10.

A: The control switch is closed. B. The safe is in its normal position in the closet. C. The clock is between 1000 and 1400 hours. D. The closet door is closed. Write the switching expression and the circuit for the burglar alarm that produces a logic 1 (rings a bell) when the safe is moved and the control switch is closed, or when the closet is opened after banking hours, or when the closet is opened with the control switch. Solution: Condition 1, Safe is moved (B’) AND Control switch is closded (A) Condition 2, Closet is opened (D’) AND After banking hours (C’) Condition 3,

Solution:

((A+D’)A’)’

Closet is opened (D’) AND With the control switch (A’)

A’

Thus, BC+A’

BC (A’D)’

F

  A  D ' A ' '  BC  A '

F   A ' D ' '  BC  A ' F   A  D  BC  A ' F  ABC  AA ' BCD  A ' D F  ABC  BCD  A ' D F  ABC  A ' D

F  A, B, C , D   AB ' C 'D' A ' D '

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