Notes

Given the function F(X,Y,Z) = XZ + Z(X'+ XY), the equivalent, most simplified Boolean representation for F is
Correct Answer: c. Z

Given that F = (A + B'+ C)(D + E), which of the following represents the only correct expression for F'?
Correct Answer: b. F' = A'BC' + D'E'

Simplification of the Boolean expression (A+B+C) + (A+B+C)'(D+E) yields which of the following results?
Correct Answer: b. A+B+C+D+E

Identify the function which generates the K-map shown
Correct Answer: c. F= Sum m(1,3,5,6)

Which of the following canonical expressions is generated by the NOR gate shown?
Correct Answer: d. F = m0

10111 is the two's complement representation of:
Correct Answer: a. -9

Simplification of the Boolean expression AB + A(BC)' yields which of following results?
Correct Answer: d. A

The two's complement of the number (01010)2 is:
Correct Answer: c. 10110

The most simple SOP expression which can be obtained from the K-map illustrated is:
Correct Answer: d. A' + B

00111 is the two's complement representation of:
Correct Answer: d. +7

Converting (0111011.100)2 to base 16 yields which of the following results?
Correct Answer: e. 3B.8

Converting (.375)10 to base 2 yields which of the following results?
Correct Answer: b. 0.011

Using the Quine-McCluskey & Petricks Method find all minimum sum-of-products expressions of f(A,B,C,D) = SUM m(1,3,5,6,8,9,12,14,15) + SUM d(4,10,13).
Correct Answers: f = A'B'D + BD' + AB + C'D + AD'
f = A'B'D + BD' + AB + BC' + AC'
f = A'B'D + BD' + AB + AC' + C'D

The most reduced expression which can be obtained from the K-map illustrated is:
Correct Answer: b. A

The truth table shown may be expressed by which of the following canonical representations?
Correct Answer: a. SUM m(2,4,6)

Identify the most simple SOP expression from the K-map shown.
Correct Answer: c. A' + B'

Given that F = SUM m(0,1,4,5,6), which of the following correctly describes F'?
Correct Answer: a. F' = SUM m(2,3,7)

Which of the following expressions is the only correct canonical representation for the function F(x,y,z) = y?
Correct Answer: c. F = SUM m(2,3,6,7)

Identify the most simple POS expression which generates the K-map shown.
Correct Answer: c. (A'+B')(A'+C)(B'+C)

Simplification of the Boolean expression AB + ABC + ABCD + ABCDE + ABCDEF yields which of the following results?
Correct Answer: c. AB

Simplification of the Boolean expression AB + A(BC)' yields which of following results?
Correct Answer: d. A

Given the function F(X,Y,Z) = XZ + Z(X'+ XY), the equivalent, most simplified Boolean representation for F is
Correct Answer: b. Z

Simplification of the Boolean expression (A + B)'(C + D + E)' + (A + B)' yields which of the following results?
Correct Answer: a. A'B'

An equivalent representation for the Boolean expression A' + 1 is
Correct Answer: b. 1

Simplification of the Boolean expression (A+B+C) + (A+B+C)'(D+E) yields which of the following results?
Correct Answer: c. A+B+C+D+E

Simplification of the Boolean expression AB + ABC + ABCD + ABCDE + ABCDEF yields which of the following results?
Correct Answer: a. AB

Simplification of the Boolean expression (A+B+C)(D+E)' + (A+B+C)(D+E) yields which of the following results?
Correct Answer: a. A + B + C

An equivalent representation for the Boolean expression A + A' is
Correct Answer: c. 1

Given that F = (A + B'+ C)(D + E), which of the following represents the only correct expression for F'?
Correct Answer: d. F' = A'BC' + D'E'

Given that F = A'B'+ C'+ D'+ E', which of the following represent the correct expression for F'?
Correct Answer: a. F'= (A+B)CDE

Given that F = SUM m(0,2,4,6), which of the following correctly describes F'?
Correct Answer: d. F' = PRD M(0,2,4,6)

Which of the following expressions is the only correct canonical representation for the function F(x,y,z) = y?
Correct Answer: d. F = SUM m(2,3,6,7)

Given that F = SUM m(0,1,4,5,6), which of the following correctly describes F'?
Correct Answer: b. F' = SUM m(2,3,7)

Minterm m31 must be represented by at least how many literals?
Correct Answer: c. 5

Given that F1 = SUM m(1,2,4,6,7) and F2 = PRD M(3,5,6) which of the following represent the only correct expression for F1*F2?
Correct Answer: d. F1*F2 = PRD M(0,3,5,6)

(mi)' + Mi = ?
Correct Answer: c. Mi

The truth table shown may be expressed by which of the following canonical representations?
Correct Answer: a. SUM m(2,4,6)

The truth table shown may be expressed by which of the following canonical expressions?
Correct Answer: c. PRD M(1,4,5,7)

The expression AB'C' is represented by which of the following cananonical symbols?
Correct Answer: b. m4

Which of the following canonical expressions is generated by the NOR gate shown?
Correct Answer: b. F = m0

Identify the most simple POS expression which generates the K-map shown.
Correct Answer: b. A'+B')(A'+C)(B'+C)

12 The most simple expression which can be obtained from the K-map illustrated is:
Correct Answer: a. 1

The most simple expression which can be obtained from the K-map shown is:
Correct Answer: b. B

Identify the most simple SOP expression from the K-map shown.
Correct Answer: a. BC' + BD' +AC'D'

Identify the most simple SOP expression from the K-map shown.
Correct Answer: d. A' + B'

The most simple SOP expression which can be obtained from the K-map illustrated is:
Correct Answer: c. A' + B

The most reduced expression which can be obtained from the K-map illustrated is:
Correct Answer: d. B'D' + BD

Identify the most simple SOP expression which generates the Karnaugh map shown:
Correct Answer: d. A'C' + B'C + ABD'

The most reduced expression which can be obtained from the K-map illustrated is:
Correct Answer: c. A

Identify the function which generates the K-map shown
Correct Answer: a. F= Sum m(1,3,5,6)

Using Quine-McCluskey method, which are prime implicants for
f(A,B,C,D,E)=SUM m(0,1,2,3,4,8,9,10,11,19,21,22,23,27,28,29,30)
Correct Answers: ACD'E
AB'CD
ABCD'
ABCE'
ACDE'
A'C'
AB'CE
C'DE
A'B'D'E'
AB'DE

Using the Quine-McCluskey & Petricks Method find all minimum sum-of-products expressions of f(A,B,C,D) = SUM m(1,3,5,6,8,9,12,14,15) + SUM d(4,10,13).
Correct Answers: f = A'B'D + BD' + AB + AC' + C'D
f = A'B'D + BD' + AB + C'D + AD'
f = A'B'D + BD' + AB + BC' + AC'

Assume the inverters have a delay of 1 ns and the other gates have a delay of 2 ns. Initially A = B = 0 an D = 1. C changes from 1 to 0 at time 2 ns. Complete the timing diagram.
Correct Answers: F4-5?
F5-6?
F6-7?
F7-8?
G1-2?
G2-3?
G3-4?
G4-5?
H6-7?

For the circuit, assume that the inverters have a delay of 1 ns and the other gates have a delay of 2 ns. Initially A=0 and B = D = 1, can C hanges from 1 to 0 at time = 2 ns. Draw the timing diagram.
Place a check iff (if and only if) the signal is high.
Correct Answers: E1-2?
E2-3?
E3-4?
F5-6?
F6-7?
F7-8?
G1-2?
G2-3?
G3-4?
G4-5?
G5-6?

Complete the timing diagram for the given circuit. Assume that both gates have a propagation delay of 5 ns.
Place a check iff (if and only if) the signal is high.
Correct Answers: V15-20?
V20-25?
Z20-25?
Z25-30?
Z30-35?

Given the following truth table:
Realize the circuit using a PLA (specify the PLA table)
Question Correct Match
1? e. 1 0 - -
2? a. 0 1 - -
3? c. 1 1 - -
4? d. 0 - 1 0
5? f. 0 - 1 1
6? b. 0 - 0 1

Use a 4-to-1 multiplexer to realize the function F(w,x,y,z) = SUM m(3,4,5,7,10,14) + SUM d(1,6,15)
Question Correct Match
I0? I. x
I1? III. 1
I2? IV. y
I3? V. 0

A circuit has four inputs RSTU and four outputs VWYZ. RSTU represents a binary-coded-decimal digit. VW represents the quotient and YZ the remainder when RSTU is divided by 3 (VW and YZ represent 2-bit binary numbers) assume that invalid inputs do not occur. Realize the circuit using a ROM.
Question Correct Match
0? X. 0000
1? IX. 0001
2? III. 0010
3? I. 0100
4? XV. 0101
5? VIII. 0110
6? VII. 1000
7? XVI. 1001
8? II. 1010
9? VI. 1100

The timing diagram corresponds to
Correct Answer: b. D latch

The PRE and CLR (preset & clear) inputs of a master/slave JK flip-flop overide the JK inputs
Correct Answer: a. Unconditionally.

The timing diagram corresponds to
Correct Answer: b. positive edge triggered

Which of the following will correctly complete the D flip-flop transition table shown below?
D Qn | Qn+1
-----|-----
0 0 | ?
0 1 | ?
1 0 | ?
1 1 | ?
Correct Answer: d. 0
0
1
1

Which of the following will correctly complete the JK flip-flop transition table shown below?
J K Qn | Qn+1
-------|-----
0 0 0 | ?
0 1 1 | ?
1 0 1 | ?
1 1 1 | ?
Correct Answer: c. 0
0
1
0

Which of the following will correctly complete the JK flip-flop transition table shown below?
J K Qn | Qn+1
-------|-----
0 0 0 | ?
0 1 0 | ?
1 0 0 | ?
1 1 0 | ?
Correct Answer: e. 0
0
1
1

For the flip flops the output state is only observed at select times (indicated by the dashed lines). What is the appropriate output sequence given that the initial (starting) state = 0.
Correct Answer: e. 001011

Which of the following will correctly complete the SR flip-flop transition table shown below?
Qn S R | Qn+1
-------|-----
0 0 0 | ?
0 0 1 | ?
0 1 0 | ?
0 1 1 | ?
1 0 0 | ?
1 0 1 | ?
1 1 0 | ?
1 1 1 | ?
Correct Answer: e. 0
0
1
indeterminate
1
0
1
indeterminate

For the flip flops the output state is only observed at select times (indicated by the dashed lines). What is the appropriate output sequence given that the initial (starting) state = 0.
Correct Answer: d. 01001

Which of the following will correctly complete the T flip-flop transition table shown below?
Qn T | Qn+1
-----|-----
0 0 | ?
0 1 | ?
1 0 | ?
1 1 | ?
Correct Answer: e. 0
1
1
0

For the flip flops the output state is only observed at select times (indicated by the dashed lines). What is the appropriate output sequence given that the initial (starting) state = 0.
Correct Answer: a. 01001

Given that F = SUM m(0,1,4,5,6), which of the following correctly describes F'?
Correct Answer: a. F' = SUM m(2,3,7)

00111 is the two's complement representation of:
Correct Answer: a. +7

Which of the following canonical expressions is generated by the NOR gate shown?
Correct Answer: b. F = m0

Identify the function which generates the K-map shown
Correct Answer: a. F= Sum m(1,3,5,6)

Converting (0111011.100)2 to base 16 yields which of the following results?
Correct Answer: a. 3B.8

Given the function F(X,Y,Z) = XZ + Z(X'+ XY), the equivalent, most simplified Boolean representation for F is
Correct Answer: d. Z

Simplification of the Boolean expression (A+B+C) + (A+B+C)'(D+E) yields which of the following results?
Correct Answer: d. A+B+C+D+E

Use a 4-to-1 multiplexer to realize the function F(w,x,y,z) = SUM m(3,4,5,7,10,14) + SUM d(1,6,15)
Question Correct Match
I0? I. x
I1? VI. 1
I2? II. y
I3? IV. 0

Converting (.375)10 to base 2 yields which of the following results?
Correct Answer: c. 0.011

Simplification of the Boolean expression AB + ABC + ABCD + ABCDE + ABCDEF yields which of the following results?
Correct Answer: c. AB

Identify the most simple SOP expression from the K-map shown.
Correct Answer: a. BC' + BD' +AC'D'

For the flip flops the output state is only observed at select times (indicated by the dashed lines). What is the appropriate output sequence given that the initial (starting) state = 0.
Correct Answer: b. 001011

Using the Quine-McCluskey & Petricks Method find all minimum sum-of-products expressions of f(A,B,C,D) = SUM m(1,3,5,6,8,9,12,14,15) + SUM d(4,10,13).
Correct Answers: f = A'B'D + BD' + AB + AC' + C'D
f = A'B'D + BD' + AB + BC' + AC'
f = A'B'D + BD' + AB + C'D + AD'

Simplification of the Boolean expression AB + A(BC)' yields which of following results?
Correct Answer: c. A