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Test: Boolean Functions - Electronics and Communication Engineering (ECE) MCQ


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10 Questions MCQ Test - Test: Boolean Functions

Test: Boolean Functions for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Test: Boolean Functions questions and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus.The Test: Boolean Functions MCQs are made for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Boolean Functions below.
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Test: Boolean Functions - Question 1

Simplify the following Boolean function in sum of minterm:
F(A, B, C, D) = Σ(0, 6, 8, 13, 14)
d (A, B, C, D) = Σ(2, 4, 10)
where, d stands for don't care condition

Detailed Solution for Test: Boolean Functions - Question 1
  • we are given the boolean function
  • we need to simplify the function in the sum of minterms
  • we will use the K-Map to simplify the function 
  • the K-Map is a very useful tool to simplify long boolean expressions into simplified form in a very systematic approach

From the K-Map we get 

  • F(A, B, C, D) = Σ(0, 6, 8, 13, 14)
  • d (A, B, C, D) = Σ(2, 4, 10)


Test: Boolean Functions - Question 2

A = a1a0 and B = b1b0 are two 2-bit unsigned binary numbers. If F(a1, a0, b1, b0) is a Boolean function such that F = 1 only when A > B, and F = 0 otherwise, then F can be minimized to the form ______

Detailed Solution for Test: Boolean Functions - Question 2

A = a1 a B = b1 b0
The Boolean function S satisfies the condition,
If A> B then  = 1.
We can represent the above condition through a truth table.



By using k-maps

Minimized form:

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Test: Boolean Functions - Question 3

In Boolean algebra A + (B.C) = ?

Detailed Solution for Test: Boolean Functions - Question 3

Logic: From the option we will find the question.
(A+B) (A+C) = A.A + A.C + B.A + B.C
Since A.A = A, the above expression becomes:
= A + A.C + A.B + B.C
= A(1 + C + B) + B.C
Since 1 + any variable = 1, the above expression becomes:
= A + B.C
(A+B) (A+C) = A + B.C

Test: Boolean Functions - Question 4

Simplify the following Boolean function:

Detailed Solution for Test: Boolean Functions - Question 4


The above equation can also be written as :

Hence option 3 is correct
Formulae:

Test: Boolean Functions - Question 5

The Boolean expression  simplifies to

Detailed Solution for Test: Boolean Functions - Question 5

De Morgan’s law states that:

Applying the De-Morgans theorem in the above function F

Hence option (4) is correct.

Test: Boolean Functions - Question 6

How many different Boolean functions of n variables are there?

Detailed Solution for Test: Boolean Functions - Question 6

Any variable 'a' can have 2 value i.e, 0 or 1.
For 'n' variables there are 2n entries in the truth table.
And each output of any particular row in the truth table can be 0 or 1.
Hence, we have 22n  different Boolean functions with n variables.
Let's understand with the help of an example - 
Let's say there are 2 variables a, and b: n = 2
There are  22 entries in the truth table, and each entry can be 0 or 1
So, we have  222 = 16  different Boolean functions with 2 variables.

Test: Boolean Functions - Question 7

Which of the following is equivalent to the Boolean function X + XY?

Detailed Solution for Test: Boolean Functions - Question 7

All Boolean algebra laws are shown below


The given Boolean function can be simplified as :
Z =  X + XY
Z = X (1 + Y)
Z = X 

Test: Boolean Functions - Question 8

If X = 1 in the logic equation  then

Detailed Solution for Test: Boolean Functions - Question 8

Let,

Test: Boolean Functions - Question 9

The equivalence of given expression x + x'y with Boolean theorem is ____.

Detailed Solution for Test: Boolean Functions - Question 9

To solve X+X'Y
Use X.1 = X, 
= X.1 + X'Y 
Use 1 + Y = 1
= X(1 + Y) + X'Y 
= X + XY + X'Y
= X + Y(X + X')
Use X + X' = 1 
= X + Y.1
Use Y.1 = Y
= X + Y
Hence answer is X+Y.

Test: Boolean Functions - Question 10

Logical expression (A+B) (A+C) is equal to

Detailed Solution for Test: Boolean Functions - Question 10

Given logical expression can be written as:
(A+B) (A+C) = A.A + A.C + B.A + B.C
Since A.A = A, the above expression becomes:
= A + A.C + A.B + B.C
= A(1 + C + B) + B.C
Since 1 + any variable = 1, the above expression becomes:
= A + B.C
(A+B) (A+C) = A + B.C

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