Digital Logic & Number representation

Question 31

Consider the equation (123)5 = (x8)y with x and y as unknown. The number of possible solutions is _____ .

• 1
• 2
• 3
• 4

Question 32

Consider the following minterm expression for F : F(P,Q,R,S) = ∑ (0, 2, 5, 7, 8, 10, 13, 15) The minterms 2, 7, 8 and 13 are \'do not care\' terms. The minimal sum-of-products form for F is :

• QS\' + Q\'S
• Q\'S\' + QS
• Q\'R\'S\' + Q\'RS\' + QR\'S + QRS
• P\'Q\'S\' + P\'QS + PQS + PQ\'S\'

Question 33

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.

C

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?

• Full adder
• Priority encoder
• Multiplexer
• Flip-flop

Question 34

[caption width="800"] [/caption]

The above sequential circuit is built using JK flip-flops is initialized with Q2Q1Q0 = 000. The state sequence for this circuit for the next 3 clock cycle is

• 001, 010, 011

• 111, 110, 101

• 100, 110, 111

• 100, 011, 001

Question 35

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

• P + Q
• (P + Q)\'
• P X Q
• (P X Q)\'

Question 36

Consider the circuit above. Which one of the following options correctly represents f (x, y, z)?

• xz\' + xy + y\'z
• xz\' + xy + (yz)\'
• xz + xy + (yz)\'
• xz + xy\' + y\'z

Question 37

Given two three bit numbers a2a1a0 and b2b1b0 and c, the carry in, the function that represents the carry generate function when these two numbers are added is:

• A
• B
• C
• D

Question 38

Consider the circuit in the diagram. The ⊕ operator represents Ex-OR. The D flipflops are initialized to zeroes (cleared).

 The following data: 100110000 is supplied to the “data” terminal in nine clock cycles. After that the values of q2q1q0 are:

• 000

• 001

• 010

• 101

Question 39

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?

• w\'xz, wxy\', xy\'z, xyz,wyz

• wxy,w\'xz,wyz

• wx(yz)\', xz, wx\'yz

• wzy, wyz, wxz, w\'xz, xy\'z, xyz

Question 40

We consider the addition of two 2’s complement numbers b_n-1b_n-2...b₀ and a_n-1a_n-2...a₀. A binary adder for adding unsigned binary numbers is used to add the two numbers. The sum is denoted by c_n-1c_n-2...c₀ and the carry-out by c_out. Which one of the following options correctly identifies the overflow condition?

• A
• B
• C
• D