21.  A circuit outputs a digit in the form of 4 bits. 0 is represented by 0000, 1 by 0001, ..., 9 by 1001. A combinational circuit is to be designed which takes these 4 bits as input and outputs 1 if the digit ≥ 5, and 0 otherwise. If only AND, OR and NOT gates may be used, what is the minimum number of gates required? 
Discuss 
Answer: (b).3

22.  Which are the essential prime implicants of the following Boolean function? f(a, b, c) = a'c + ac' + b'c 
Discuss 
Answer: (a).a'c and ac'

23.  Consider a multiplexer with X and Y as data inputs and Z as control input. Z = 0 selects input X, and Z = 1 selects input Y. What are the connections required to realize the 2variable Boolean function f = T + R, without using any additional hardware ? 
Discuss 
Answer: (a).R to X, 1 to Y, T to Z

24.  A 4bit carry lookahead adder, which adds two 4bit numbers, is designed using AND, OR, NOT, NAND, NOR gates only. Assuming that all the inputs are available in both complemented and uncomplemented forms and the delay of each gate is one time unit, what is the overall propagation delay of the adder? Assume that the carry network has been implemented using twolevel ANDOR logic. 
Discuss 
Answer: (a).4 time units

25.  Consider an array multiplier for multiplying two n bit numbers. If each gate in the circuit has a unit delay, the total delay of the multiplier is 
Discuss 
Answer: (c).Θ(n)

26.  A 1input, 2output synchronous sequential circuit behaves as follows : Let zk, nk denote the number of 0's and 1's respectively in initial k bits of the input (zk + nk = k). The circuit outputs 00 until one of the following conditions holds. zk  nk = 2. In this case, the output at the kth and all subsequent clock ticks is 10. nk  zk = 2. In this case, the output at the kth and all subsequent clock ticks is 01. What is the minimum number of states required in the state transition graph of the above circuit? 
Discuss 
Answer: (a).5

27.  Let f(A, B) = A' + B. Simplified expression for function f(f(x + y, y)z) is : 
Discuss 
Answer: (c).xy' + z

28.  Consider a 4 bit Johnson counter with an initial value of 0000. The counting sequence of this counter is: 
Discuss 
Answer: (d).0, 8, 12, 14, 15, 7, 3, 1, 0

29.  A positive edgetriggered D flipflop is connected to a positive edgetriggered JK flipflop as follows. The Q output of the D flipflop is connected to both the J and K inputs of the JK flipflop, while the Q output of the JK flipflop is connected to the input of the D flipflop. Initially, the output of the D flipflop is set to logic one and the output of the JK flipflop is cleared. Which one of the following is the bit sequence (including the initial state) generated at the Q output of the JK flipflop when the flipflops are connected to a freerunning common clock? Assume that J = K = 1 is the toggle mode and J = K = 0 is the stateholding mode of the JK flipflop. Both the flipflops have nonzero propagation delays. 
Discuss 
Answer: (a).0110110...

30.  Consider the operations f(X, Y, Z) = X'YZ + XY' + Y'Z' and g(X′, Y, Z) = X′YZ + X′YZ′ + XY. Which one of the following is correct? 
Discuss 
Answer: (b).Only {f} is functionally complete
