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

32.  The number of minterms after minimizing the following Boolean expression is _________. [D′ + AB′ + A′C + AC′D + A′C′D]′ 
Discuss 
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 4bit ripplecarry binary adder is implemented by using full adders. The total propagation time of this 4bit binary adder in microseconds is 
Discuss 
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 ________. 
Discuss 
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? 
Discuss 
Answer: (a).S1False, S2True, S3True, S4False

36.  What is the minimum number of NAND gates required to implement a 2input EXCLUSIVEOR function without using any other logic gate? 
Discuss 
Answer: (b).4

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

38.  The number (123456)8 is equivalent to 
Discuss 
Answer: (a).(A72E)16 and (22130232)4

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

40.  Which of the following expressions is equivalent to (A⊕B)⊕C 
Discuss 
Answer: (c).ABC+A¯(B⊕C)+B¯(A⊕C)
