Digital Logic Gate Previous Year Questions



Ques 1Digital Logic

Consider a digital display system (DDS) shown in the figure that displays the contents of register X. A 16-bit code word is used to load a word in X, either from S or from R. S is a 1024-word memory segment and R is a 32-word register file. Based on the value of mode bit M, T selects an input word to load in X. P and Q interface with the corresponding bits in the code word to choose the addressed word. Which one of the following represents the functionality of P, Q, and T?

a) P is 10:1 multiplexer; Q is 5:1 multiplexer; T is 2:1 multiplexer
b) P is 10:210 decoder; Q is 5:25 decoder; T is 2:1 encoder
c) P is 10:210 decoder; Q is 5:25 decoder; T is 2:1 multiplexer
d) P is 1:10 de-multiplexer; Q is 1:5 de-multiplexer; T is 2:1 multiplexer


c is the correct answer.




Ques 2Digital Logic

The following simple undirected graph is referred to as the Peterson graph


Which of the following statements is/are TRUE?

a) The chromatic number of the graph is 3.
b) The graph has a Hamiltonian path.
c) The following graph is isomorphic to the Peterson graph.

d) The size of the largest independent set of the given graph is 3. (A subset of vertices of a graph form an independent set if no two vertices of the subset are adjacent.)


c is the correct answer.




Ques 3Digital Logic

Let R1 and R2 be two 4-bit registers that store numbers in 2’s complement form. For the operation R1+R2, which one of the following values of R1 and R2 gives an arithmetic overflow?

a) R1 = 1011 and R2 = 1110
b) R1 = 1100 and R2 = 1010
c) R1 = 0011 and R2 = 0100
d) R1 = 1001 and  R2 = 1111


b is the correct answer.




Ques 4Digital Logic

Let the representation of a number in base 3 be 210. What is the hexadecimal representation of the number?

a) 15
b) 588
c) D2
d) 528


a is the correct answer.




Ques 5Digital Logic

If there are m input lines n output lines for a decoder that is used to uniquely address a byte addressable 1 KB RAM, then the minimum value of m+n is ________ .


1024 is the correct answer.




Ques 6Digital Logic

In 16-bit 2’s complement representation, the decimal number −28 is:

a) 1111 1111 0001 1100
b) 0000 0000 1110 0100
c) 1111 1111 1110 0100
d) 1000 0000 1110 0100


c is the correct answer.




Ques 7Digital Logic

What is the minimum number of 2-input NOR gates required to implement 4-variable function expressed in sum-of-minterms from as f = Σ(0, 2, 5, 7, 8, 10, 13, 15)? Assume that all the inputs and their complements are available. Answer ________


3 is the correct answer.




Ques 8Digital Logic

Two numbers are chosen independently and uniformly at random from the set {1, 2, ..., 13}. The probability (rounded off to 3 decimal places) that their 4-bit (unsigned) binary representations have the same most significant bit is ___________.


a is the correct answer.




Ques 9Digital Logic

Consider the minterm list form of a Boolean function F given below.

F(P, Q, R, S) = Σm(0, 2, 5, 7, 9, 11) + d(3, 8, 10, 12, 14)


Here, m denotes a minterm and d denotes a don^^t care term. The number of essential prime implicants of the function F is ______ .


a is the correct answer.




Ques 10Digital Logic

Given the following binary number in 32 bit (single precision) IEEE-754 format:

00111110011011010000000000000000

The decimal value closest to this floating-point number is:

a) 1.45 X 101

b) 1.45 X 10-1

c) 2.27 X 10-1

d) 2.27 X 101


Number Representation is the correct answer.




Ques 11Digital Logic

When two 8-bit numbers A7 ... A0 and B7 ... B0 in 2^^s complement representation (with A0 and B0 as the least significant bits) are added using ripple-carry adder. the sum bits obtained are S7 ... S0 and the carry bits are C7 ... C0. An overflow is said to have occurred if

a) the carry bit C7 is 1
b) all the carry bits (C7, ... , C0 ) are 1
c) (A7 . B7 . S7' + A7' . B7' . S7) is 1
d) (A0 . B0 . S0' + A0' . B0' . S0) is 1


Complements is the correct answer.




Ques 12Digital Logic

The width of the physical address on a machine is 40 bits. The width of the tag field in a 512 KB 8-way set associative cache is ____________ bits.


a is the correct answer.




Ques 13Digital Logic

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 is the correct answer.




Ques 14Digital Logic

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 is the correct answer.




Ques 15Digital Logic

Let, x1⊕x2⊕x3⊕x4= 0 where x1, x2, x3, x4 are Boolean variables, and ⊕ is the XOR operator. Which one of the following must always be TRUE ?

a) x1x2x3x4=0
b) x1x3+x4=0
c) x'1⊕x'3=x'2⊕x'4
d) x1+x2+x3+x4=0


Logic Gates is the correct answer.




Ques 16Digital Logic

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 is the correct answer.




Ques 17Digital Logic

The 16-bit 2’s complement representation of an integer is 1111 1111 1111 0101; its decimal representation is


a is the correct answer.




Ques 18Digital Logic

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)


Full Adder is the correct answer.




Ques 19Digital Logic

Consider the Boolean operator # with the following properties:

x#0 = x, x#1 = x', x#x = 0 and x#x'= 1

Then x#y is equivalent to

a) x'y + xy'
b) xy' + (xy)
c) x'y + xy
d) xy + (xy)'


Boolean operator is the correct answer.




Ques 20Digital Logic

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 is the correct answer.




Ques 21Digital Logic

Consider a 4 bit Johnson counter with an initial value of 0000. The counting sequence of this counter is

a) 0,1,3,7,15,14,12,8,0
b) 0,2,4,6,8,10,12,14,0
c) 0,8,12,14,15,7,3,1,0
d) 0,1,3,5,7,9,11,13,15,0


Number Representation is the correct answer.




Ques 22Digital Logic

Which one of the following is NOT equivalent to p ↔ q?

a) (┐p ˅ q) ˄ (p ˅ ┐q)
b) (┐p ˅ q) ˄ (q → p)
c) (┐p ˄ q) ˅ (p ˄ ┐q)
d) (┐p ˄ ┐q) ˅ (p ˄ q)


Proposition Logic is the correct answer.




Ques 23Digital Logic

Consider the following Boolean expression for F:

F(P, Q, R, S) = PQ + P'QR + P'QR'S

The minimal sum-of-products form of F is__________

a) PQ + QR + QS
b) P + Q + R + S
c) P’ + Q’ + R’ + S’
d) P’R + P’R’S + P


Logic Function and Minimization is the correct answer.