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31. The minimum number of JK flip-flops required to construct a synchronous counter with the count sequence (0, 0, 1, 1, 2, 2, 3, 3, 0, 0,...) is ________.
a. 0
b. 1
c. 2
d. 3
Answer: (d).3

32. The number of min-terms after minimizing the following Boolean expression is _________.

[D′ + AB′ + A′C + AC′D + A′C′D]′
a. 1
b. 2
c. 3
d. 4
Answer: (a).1

33. A half adder is implemented with XOR and AND gates. A full adder is implemented with two half adders and one OR gate. The propagation delay of an XOR gate is twice that of an AND/OR gate. The propagation delay of an AND/OR gate is 1.2 microseconds. A 4-bit ripple-carry binary adder is implemented by using full adders. The total propagation time of this 4-bit binary adder in microseconds is
a. 19.2 microseconds
b. 18.0 microseconds
c. 12.3 microseconds
d. 16.6 microseconds
Answer: (a).19.2 microseconds

34. The total number of prime implicants of the function f(w, x, y, z) = Σ(0, 2, 4, 5, 6, 10) is ________.
a. 2
b. 3
c. 4
d. 5
Answer: (b).3

35. Given the function F = P′ + QR, where F is a function in three Boolean variables P, Q and R and P′ = !P, consider the following statements.

S1: F = Σ (4, 5, 6)
S2: F = Σ (0, 1, 2, 3, 7)
S3: F = Π (4, 5, 6)
S4: F = Π (0, 1, 2, 3, 7)

Which of the following is true?
a. S1-False, S2-True, S3-True, S4-False
b. S1-True, S2-False, S3-False, S4-True
c. S1-False, S2-False, S3-True, S4-True
d. S1-True, S2-True, S3-False, S4-False
Answer: (a).S1-False, S2-True, S3-True, S4-False

36. What is the minimum number of NAND gates required to implement a 2-input EXCLUSIVE-OR function without using any other logic gate?
a. 3
b. 4
c. 5
d. 6
Answer: (b).4

37. Using a 4-bit 2’s complement arithmetic, which of the following additions will result in an overflow? (i) 1100 + 1100 (ii) 0011 + 0111 (iii) 1111 + 0111
a. (i) only
b. (ii) only
c. (iii) only
d. (i) and (iii) only
Answer: (b).(ii) only

38. The number (123456)8 is equivalent to
a. (A72E)16 and (22130232)4
b. (A72E)16 and (22131122)4
c. (A73E)16 and (22130232)4
d. (A62E)16 and (22120232)4
Answer: (a).(A72E)16 and (22130232)4

39. The function AB’C + A’BC + ABC’ + A’B’C + AB’C’ is equivalent to
a. AC’+AB+A’C
b. AB’+AC’+A’C
c. A’B+AC’+AB'
d. A’B+AC+AB'
Answer: (b).AB’+AC’+A’C

40. Which of the following expressions is equivalent to (A⊕B)⊕C
a. (A+B+C)(A¯+B¯+C¯)
b. (A+B+C)(A¯+B¯+C)
c. ABC+A¯(B⊕C)+B¯(A⊕C)
d. None of the above
Answer: (c).ABC+A¯(B⊕C)+B¯(A⊕C)

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