41. Using Booth's Algorithm for multiplication, the multiplier -57 will be recoded as a. 0 -1 0 0 1 0 0 -1 b. 1 1 0 0 0 1 1 1 c. 0 -1 0 0 1 0 0 0 d. 0 1 0 0 -1 0 0 1
 Answer: (a).0 -1 0 0 1 0 0 -1

 42. How many pulses are needed to change the contents of a 8-bit up counter from 10101100 to 00100111 (rightmost bit is the LSB)? a. 134 b. 133 c. 124 d. 123

 43. We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then repeats. The minimum number of J-K flip-flops required to implement this counter is a. 1 b. 2 c. 4 d. 5

 44. Consider a carry lookahead adder for adding two n-bit integers, built using gates of fan-in at most two. The time to perform addition using this adder is a. Θ(1) b. Θ(Log (n)) c. Θ(√ n) d. Θ(n)

 45. Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are integers represented in 2’s complement form. If the decimal value of A is one, the decimal value of B that leads to the longest latency for the sum to stabilize is _____________ a. -1 b. 2 c. 1 d. -2

 46. Let X be the number of distinct 16-bit integers in 2’s complement representation. Let Y be the number of distinct 16-bit integers in sign magnitude representation. Then X −Y is _________ a. 1 b. 2 c. 3 d. 0

 47. The addition of 4-bit, two's complement, binary numbers 1101 and 0100 results in a. 0001 and an overflow b. 1001 and no overflow c. 0001 and no overflow d. 1001 and an overflow