11. In a look-ahead carry generator, the carry generate function Gi and the carry propagate function Pi for inputs Ai and Bi are given by:

Pi = Ai ⨁ Bi and Gi = AiBi

The expressions for the sum bit Si and the carry bit Ci+1 of the look-ahead carry adder are given by:

Si = Pi ⨁ Ci and Ci+1 = Gi + PiCi , where C0 is the input carry.

Consider a two-level logic implementation of the look-ahead carry generator. Assume that all Pi and Gi are available for the carry generator circuit and that the AND and OR gates can have any number of inputs. The number of AND gates and OR gates needed to implement the look-ahead carry generator for a 4-bit adder with S3, S2, S1, S0 and C4 as its outputs are respectively:
a. 6, 3
b. 10, 4
c. 6, 4
d. 10, 5
Answer: (b).10, 4

12. Let k = 2^n. A circuit is built by giving the output of an n-bit binary counter as input to an n-to-2^n bit decoder. This circuit is equivalent to a
a. k-bit binary up counter
b. k-bit binary down counter
c. k-bit ring counter
d. k-bit Johnson counter
Answer: (c).k-bit ring counter

13. Consider the equation (123)5 = (x8)y with x and y as unknown. The number of possible solutions is _____ .
a. 1
b. 2
c. 3
d. 4
Answer: (c).3

14. Consider the following combinational function block involving four Boolean variables x, y, a, b where x, a, b are inputs and y is the output.

f (x, y, a, b)
if (x is 1) y = a;
else y = b;

Which one of the following digital logic blocks is the most suitable for implementing this function?
a. Full adder
b. Priority encoder
c. Multiplexer
d. Flip-flop
Answer: (c).Multiplexer

15. Let X denote the Exclusive OR (XOR) operation. Let ‘1’ and ‘0’ denote the binary constants. Consider the following Boolean expression for F over two variables P and Q:

F(P, Q) = ( ( 1 X P) X (P X Q) ) X ( (P X Q) X (Q X 0) )

The equivalent expression for F is
a. P + Q
b. (P + Q)'
c. P X Q
d. (P X Q)'
Answer: (d).(P X Q)'

16. Consider a Boolean function f (w, x, y, z). suppose that exactly one of its inputs is allowed to change at a time. If the function happens to be true for two input vectors i1 = (w1, x1, y1, z1) and i2 = (w2, x2, y2, z2) we would like the function to remain true as the input changes from i1 to i2 (i1 and i2 differ in exactly one bit position), without becoming false momentarily. Let f (w, x, y, z) = ∑(5,7,11,12,13,15). Which of the following cube covers of f will ensure that the required property is satisfied?
a. w'xz, wxy', xy'z, xyz,wyz
b. wxy,w'xz,wyz
c. wx(yz)', xz, wx'yz
d. wzy, wyz, wxz, w'xz, xy'z, xyz
Answer: (a).w'xz, wxy', xy'z, xyz,wyz

17. The hexadecimal representation of 6578 is
a. 1AF
b. D78
c. D71
d. 32F
Answer: (a).1AF

18. The switching expression corresponding to f(A, B, C, D) = Σ (1, 4, 5, 9, 11, 12) is
a. BC'D' + A'C'D + AB'D
b. ABC' + ACD + B'C'D
c. ACD' + A'BC' + AC'D'
d. A'BD + ACD' + BCD'
Answer: (a).BC'D' + A'C'D + AB'D

19. The Boolean function x'y' + xy + x'y is equivalent to
a. x' + y'
b. x + y
c. x + y'
d. x' + y
Answer: (d).x' + y

20. In an SR latch made by cross-coupling two NAND gates, if both S and R inputs are set to 0, then it will result in
a. Q = 0, Q' = 1
b. Q = 1, Q' = 0
c. Q = 1, Q' = 1
d. Indeterminate states
Answer: (d).Indeterminate states

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