Phrases Boolean algebra Previous Year Question Paper and Solution with PDF

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Phrases Previous Year Questions (PYQs)

Phrases Boolean Algebra PYQ

Qus : 1

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

Qus : 2

Which term is redundant in the expression AB + A'C + BC ?

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Solution

Qus : 3

The total number binary function that can be defined using n Boolean variables is

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Solution

✅ Given Information:

We are asked to find the total number of binary functions that can be defined using n Boolean variables.

✅ Step 1: Number of input combinations:

For n Boolean variables, the number of possible input combinations is 2ⁿ.

✅ Step 2: Number of possible outputs:

Each input combination can map to either 0 or 1, so there are 2 possible outputs for each of the 2ⁿ input combinations.

✅ Final Formula:

Total Binary Functions = 2^(2ⁿ)

✅ Final Answer:

The total number of binary functions that can be defined using n Boolean variables is: 2^(2ⁿ)

Qus : 4

Assume x' represents negation of x the Boolean function x'y' + xy + x'y is equivalent to?

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Solution

Qus : 5

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)

Qus : 6

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

Qus : 7

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

Qus : 8

The number of minterms in a

$n$ variable truth tableis

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Solution

✅ Number of Minterms in a n-variable Truth Table:

For n Boolean variables, the number of possible combinations of inputs is:

2ⁿ

Each combination corresponds to one minterm. Therefore, the total number of minterms in the truth table is also 2ⁿ.

✅ Final Answer:

The number of minterms in a n-variable truth table is: 2ⁿ

Qus : 9

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

Qus : 10

The reduced form of the Boolean function F = xyz + xyz' + x'y'z + xy'z is

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Solution

Qus : 11

How many Boolean expressions can be formed with 3 Boolean variables?

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Solution

Qus : 12

Any given truth table can be represented by

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Solution

Qus : 13

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)

Qus : 14

The Boolean expression for the following truth table is _________

x	y	z	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

Qus : 15

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

$AB+A\, \overline{B}C+A\, \overline{B}\, \overline{C}$

$AB+AB'C+AB'C'$

$AB+AB'(C+C')$

$AB+AB'$

$A(B+B')$

Qus : 16

Which of the following is equivalent to the Boolean expression:

$(X+Y).(X+\overline{Y}).(\overline{X}+Y)$

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Solution

$(X+Y).(X+\overline{Y}).(\overline{X}+Y)$

$(X+Y)(X+Y')(X'+Y)$

$(XX+XY+YX+YY')(X'+Y)$

$(X+XY)(X'+Y)$

$X(1+Y)(X'+Y)$

$X(X'+Y)$

$XX'+XY$

$XY$

Qus : 17

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

Qus : 18

The Boolean expression AB+ AB' + A'C + AC is unaffected by the value of the Boolean variable

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Solution

$\begin{array}{ll}{A(B+\overline{B})+C(A+\overline{A})} \\ {A+C}\, \end{array}$

Qus : 19

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

Table representing NAND Gate.

Qus : 20

The number of terms in the product of sums canonical form of

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Solution

Qus : 21

Consider 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

Qus : 22

The Boolean expression represented by the following Venn diagram is

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Solution

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Phrases Previous Year Questions (PYQs)

Phrases Boolean Algebra PYQ

Solution

Solution

Solution

✅ Given Information:

✅ Step 1: Number of input combinations:

✅ Step 2: Number of possible outputs:

✅ Final Formula:

✅ Final Answer:

Solution

Solution

Solution

Solution

Solution

✅ Number of Minterms in a n-variable Truth Table:

✅ Final Answer:

Solution

Solution

Solution

Solution

Solution

Boolean Simplification

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

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