Digital Logic - Online Test
Q1. The truth table
represents the Boolean function
Answer : Option A
Explaination / Solution:
XY'+ XY = X(Y'+ Y) = X
Q2. Consider the set of strings on {0,1} in which, every substring of 3 symbols has at most two
zeros. For example, 001110 and 011001 are in the language, but 100010 is not. All strings of
length less than 3 are also in the language. A partially completed DFA that accepts this
language is shown below.
The missing arcs in the DFA are
Answer : Option D
Explaination / Solution:
The complete DFA is
Q3. What is the minimal form of the Karnaugh map shown below? Assume that X denotes a don’t
care term.
Answer : Option B
Explaination / Solution:
Q4. Which one of the following expressions does NOT represent exclusive NOR of x and y?
Answer : Option D
Explaination / Solution:
Q5. A binary operation ⊕ on a set of integers is defined as x ⊕ y = x2 + y2. Which one of the
following statements is TRUE about ⊕?
Answer : Option A
Explaination / Solution:
x ⊕ y = x2 + y2 = y2 + x2 = y ⊕ x
∴ commutative
Not associative, since, for example
(1 ⊕ 2) ⊕ 3 ≠ 1 ⊕ (2 ⊕ 3)
Q6. Which one of the following is NOT logically equivalent to ¬∃x (∀y (α) ∧ ∀z (β))?
Answer : Option A
Explaination / Solution:
No Explaination.
Q7. 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
Answer : Option B
Explaination / Solution:
Q8. 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?
Answer : Option C
Explaination / Solution:
‘x’ is working as selection line, where the two input lines are ‘a’ and
‘b’, so the function F (x, y,a,b) can be implemented using (2× 1)
multiplexer as follows:
Q9. 
The above synchronous sequential circuit built using JK flip-flops is initialized with
Q2Q1Q0 = 000. The state sequence for this circuit for the next 3 clock cycles is
Answer : Option C
Explaination / Solution:
Q10. Let ⊕ 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⊕P)⊕(P⊕Q))⊕((P⊕Q)⊕(Q⊕0))
The equivalent expression for F is
Answer : Option D
Explaination / Solution:
