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NIMCET Previous Year Questions (PYQs)
NIMCET Boolean Algebra PYQ
Which one of the following Boolean algebraic rule is correct?
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Solution
A + A'B = (A + A') . (A + B)
= 1 . (A + B)
= A + B
The total number binary function that can be defined using n Boolean variables is
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Solution
Assume x' represents negation of x the Boolean function x'y' + xy + x'y is equivalent to?
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Solution
The equivalence of given expression x+x'y with Boolean theorem is….
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Solution
x+x'y
=(x+x')(x+y)=(x+y)
Consider the following minterm for F:F(P, Q, R, S) = Σ0, 2, 5, 7, 8, 10, 13, 15. The minterms 2, 7, 8, and 13 are don't care terms. The minimal sum of products form for F is
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Solution
Cosider the following Boolean Expression for F:
$F(P,Q,R,S)=PQ+\overline{P}QR+\overline{P}Q\overline{R}S$ .
The minimum sum of products form of F is
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Solution
Let $\oplus$ and $\odot$ denote the Exclusive - OR and Exclusive-NOR operations respectively. Which of the following is not correct?
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Solution
The reduced form of the Boolean function $F=xyz+xyz^{\prime}^{}+x^{\prime}yz+xy^{\prime}z$ is
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Solution
The expression P+QR is the reduced
form of _____
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Solution
Boolean Simplification
Given Expression: P + QR
We ask: This is the simplified (reduced) form of which expression?
Try expanding: (P + Q)(P + R)
Using distributive law:
(P + Q)(P + R) = P(P + R) + Q(P + R) = P + PR + PQ + QR = P + PQ + PR + QR = P + QR (since P absorbs PQ and PR)
✅ Final Answer: (P + Q)(P + R)
The
Boolean expression for the following truth table is _________
| x | y | x | f |
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 1 |
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Solution
The minimum number of NAND gates required for implementing the Boolean expression $AB+A\, \overline{B}C+A\, \overline{B}\, \overline{C}$
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Solution
$AB+A\, \overline{B}C+A\, \overline{B}\, \overline{C}$=$AB+AB'C+AB'C'$
=$AB+AB'(C+C')$
=$AB+AB'$
=$A(B+B')$
=A
Which of the following is equivalent to the Boolean expression:
$(X+Y).(X+\overline{Y}).(\overline{X}+Y)$
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Solution
$(X+Y).(X+\overline{Y}).(\overline{X}+Y)$
=$(X+Y)(X+Y')(X'+Y)$
=$(XX+XY+YX+YY')(X'+Y)$
=$(X+XY)(X'+Y)$
=$X(1+Y)(X'+Y)$
=$X(X'+Y)$
=$XX'+XY$
=$XY$
Write the simplified form of the Boolean expression
(A+C)(AD+AD')+AC+C
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Solution
(A+C)(AD+AD')+AC+C=(A+C)A(D+D')+C(A+1)
=(A+C)+C
=A+C
The Boolean expression AB+ AB' + A'C + AC is unaffected by the value of the Boolean variable
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Solution
$\begin{array}{ll}{A(B+\overline{B})+C(A+\overline{A})} \\ {A+C}\, \end{array}$If a signal passing through a gate is inhibited by sending a low into one of the inputs, and the output is HIGH, the gate is a(n):
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Solution
Output is high if any of the input is low. The truth table for NAND gate is:| A | B | Output |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
isConsider the following min term 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
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Solution
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