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

 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

 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

 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

 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

 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

 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