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Test: Boolean Logic Operations - GATE MCQ


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10 Questions MCQ Test - Test: Boolean Logic Operations

Test: Boolean Logic Operations for GATE 2024 is part of GATE preparation. The Test: Boolean Logic Operations questions and answers have been prepared according to the GATE exam syllabus.The Test: Boolean Logic Operations MCQs are made for GATE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Boolean Logic Operations below.
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Test: Boolean Logic Operations - Question 1
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In boolean algebra, the OR operation is performed by which properties?

Detailed Solution for Test: Boolean Logic Operations - Question 1

The expression for Associative property is given by A+(B+C) = (A+B)+C & A*(B*C) = (A*B)*C.
The expression for Commutative property is given by A+B = B+A & A*B = B*A.
The expression for Distributive property is given by A+BC=(A+B)(A+C) & A(B+C) = AB+AC.

Test: Boolean Logic Operations - Question 2
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According to boolean law: A + 1 = ?

Detailed Solution for Test: Boolean Logic Operations - Question 2

A + 1 = 1, as per 1’s Property.

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Test: Boolean Logic Operations - Question 3
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A(A + B) = ?

Detailed Solution for Test: Boolean Logic Operations - Question 3

A(A + B) = AA + AB (By Distributive Property) = A + AB (A.A = A By Commutative Property) = A(1 + B) = A*1 (1 + B = 1 by 1’s Property) = A.

Test: Boolean Logic Operations - Question 4
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(A + B)(A’ * B’) = ?
Detailed Solution for Test: Boolean Logic Operations - Question 4

The DeMorgan’s law states that (AB)’ = A’ + B’ & (A + B)’ = A’ * B’, as per the Dual Property.

Test: Boolean Logic Operations - Question 5
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Simplify Y = AB’ + (A’ + B)C.
Detailed Solution for Test: Boolean Logic Operations - Question 5

Y = AB’ + (A’ + B)C = AB’ + (AB’)’C = (AB’ + C)( AB’ + AB’) = (AB’ + C).1 = (AB’ + C).

Test: Boolean Logic Operations - Question 6
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The expression for Absorption law is given by _________
Detailed Solution for Test: Boolean Logic Operations - Question 6

The expression for Absorption Law is given by: A+AB = A.
Proof: A + AB = A(1+B) = A (Since 1 + B = 1 as per 1’s Property).

Test: Boolean Logic Operations - Question 7
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The involution of A is equal to _________
Detailed Solution for Test: Boolean Logic Operations - Question 7

The involution of A means double inversion of A (i.e. A”) and is equal to A.
Proof: ((A)’)’ = A

Test: Boolean Logic Operations - Question 8
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DeMorgan’s theorem states that _________
Detailed Solution for Test: Boolean Logic Operations - Question 8

The DeMorgan’s law states that (AB)’ = A’ + B’ & (A + B)’ = A’ * B’, as per the Dual Property.

Test: Boolean Logic Operations - Question 9
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Complement of the expression A’B + CD’ is _________
Detailed Solution for Test: Boolean Logic Operations - Question 9

(A’B + CD’)’ = (A’B)'(CD’)’ (By DeMorgan’s Theorem) = (A” + B’)(C’ + D”) (By DeMorgan’s Theorem) = (A + B’)(C’ + D).

Test: Boolean Logic Operations - Question 10
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The boolean function A + BC is a reduced form of ____________
Detailed Solution for Test: Boolean Logic Operations - Question 10

(A + B)(A + C) = AA + AC + AB + BC = A + AC + AB + BC (By Commutative Property) = A(1 + C + B) + BC = A + BC (1 + B + C =1 By 1’s Property).

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