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Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE) PDF Download

Q1: Simplified form of the Boolean function:
Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)is (2024)
(a) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)

(b) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
(c) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
(d) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
Ans: (a)
Sol: Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)Minimize function = Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)

Q2: The output expression for the Karnaugh map shown below is (2019)
Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)(a) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)

(b) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
(c) QR+SQR + S
(d) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)

Ans: (a)
Sol:
Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)Output =Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)

Q3: Digital input signals A, B, C with A as the MSB and C as the LSB are used to realize the Boolean function
F = m0 + m2 + m3 + m5 + m7, where mi
denotes the ith minterm. In addition, F has a don't care for m1. The simplified expression for F is given by  (2018)
(a) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)

(b) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
(c) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
(d) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
Ans: (b)
Sol: Given,  f = m+ m+ m+ m+ m7 and m= don't care
Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
Q4: The output expression for the Karnaugh map shown below is (SET-1(2017))
Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)(a) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)

(b) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
(c) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
(d) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
Ans: (d)
Sol: Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
Q5: The Boolean expression Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE) simplifies to  (SET-1  (2017))
(a) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)

(b) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
(c) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
(d) AB + BC
Ans:
(a)
Sol: Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
Q6: The Boolean expression Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)simplifies to (SET-2 (2016))
(a) 1
(b) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)

(c) a.b
(d) 0
Ans:
(d)
Sol: Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)F = 0

Q7: The output expression for the Karnaugh map shown below is (SET-2 (2016))
Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)(a) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)

(b) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
(c) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
(d) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
Ans: (b)
Sol: Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
Q8: Consider the following Sum of Products expression, F.Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE) The equivalent Product of Sums expression is (SET-2 (2015))
(a) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)

(b) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
(c) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
(d) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
Ans: (a)
Sol: The SOP form of F is ( shown in K-map)
Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)So,POS form can be formed using '0' from the K-map.
Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
Q9: f(A, B, C, D) = Π M(0, 1, 3, 4, 5, 7, 9, 11, 12, 13, 14, 15) is a maxterm representation of a Boolean function f(A, B, C, D) where A is the MSB and D is the LSB. The equivalent minimized representation of this function is (SET-1 (2015))
(a) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)

(b) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
(c) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
(d) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
Ans: (a)

Q10: The SOP (sum of products) form of a Boolean function is Σ(0, 1, 3, 7, 11), where inputs are A, B, C , D (A is MSB, and D is LSB). The equivalent minimized expression of the function is (SET-2  (2014))
(a) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)

(b) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
(c) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
(d) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
Ans: (a)
Sol: The 4 variable Boolean function is given in canonical sum of product form as,
 f(A, B, C, D) = Σ(0, 1, 3, 7, 11)
As the options are given in the simplified product of sum form, we first convert the given function in canonical product of sum form, as under
 f(A, B, C, D) = Π(2, 4, 5, 6, 8, 9, 10, 12, 13, 14, 15)
Now by plotting the above function on a 4 variable K-map (Maxterm map), we obtain the simplified expression of the function
Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
Q11: Which of the following is an invalid state in an 8-4-2-1 Binary Coded Decimal counter (SET-2 (2014))
(a) 1 0 0 0
(b) 1 0 0 1
(c) 0 0 1 1
(d) 1 1 0 0
Ans: 
(d)
Sol: Binary coded decimal counter counts from 0 to 9. So, 1100 is an initial state i.e. 12.

Q12: In the sum of products function f(X, Y, Z) = ∑(2, 3, 4, 5), the prime implicants are  (2012)
(a) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)

(b) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
(c) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
(d) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
Ans: (a)
Sol: f(X, Y, Z) = Σ(2, 3, 4, 5)
Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
Q13: The following Karnaugh map represents a function F.
Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)Which of the following circuits is a realization of the above function (2010)
(a) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)(b) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)(c) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)(d) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)Ans: 
(d)
Sol: From the figure, it is clear that, two NAND gates generate the Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE) and now two AND gates with i/p Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE) and inputs Y and Z is used to generate two terms of SOP form and OR gate is used to sum them and generate th F.

Q14: The following Karnaugh map represents a function F.
Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)A minimized form of the function F is  (2010)
(a) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)

(b) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
(c) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
(d) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
Ans: (b)
Sol:
Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
Q15: The simplified form of the Boolean expression Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE) can be written as (2004)
(a) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)

(b) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
(c) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
(d) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
Ans: (a)
Sol: Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
Q16: The boolean expression Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)can be simplified to (2003)
(a) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)

(b) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
(c) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
(d) Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)
Ans: (b)
Sol: By K-map
Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE)The simplified for isPrevious Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE).

The document Previous Year Questions- Boolean Algebra and Minimization | Analog and Digital Electronics - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Analog and Digital Electronics.
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FAQs on Previous Year Questions- Boolean Algebra and Minimization - Analog and Digital Electronics - Electrical Engineering (EE)

1. What is Boolean Algebra and why is it important in Electrical Engineering?
Ans.Boolean Algebra is a branch of mathematics that deals with variables that have two possible values: true (1) and false (0). It is essential in Electrical Engineering because it provides a formal framework for designing and analyzing digital circuits and systems. Boolean Algebra allows engineers to simplify complex logical expressions, making it easier to implement efficient circuit designs.
2. How do you minimize Boolean expressions using Karnaugh Maps?
Ans.Karnaugh Maps (K-maps) are a visual method for minimizing Boolean expressions. To use K-maps, you plot the truth values of the expression in a grid format. By grouping adjacent cells that contain '1's, you can find the simplest form of the expression. Each group corresponds to a product term in the minimized expression. The goal is to create the fewest groups possible to achieve the simplest logical representation.
3. What are some common laws and theorems used in Boolean Algebra?
Ans.Some common laws and theorems used in Boolean Algebra include De Morgan's Theorems, the Idempotent Law, the Dominance Law, and the Distributive Law. De Morgan's Theorems, for instance, state that the complement of a product is the sum of the complements, and vice versa. Understanding these laws is crucial for simplifying Boolean expressions and solving problems in electrical circuits.
4. What is the significance of the Quine-McCluskey algorithm in Boolean minimization?
Ans.The Quine-McCluskey algorithm is a systematic method for minimizing Boolean functions, particularly useful for functions with a large number of variables. It involves listing all possible minterms and systematically eliminating redundancies to find the simplest form of the expression. This algorithm is significant because it provides a reliable method for finding optimal solutions in cases where K-maps become cumbersome.
5. How can truth tables be used in conjunction with Boolean Algebra for circuit design?
Ans.Truth tables are used to represent the output of a logical expression for every possible input combination. When designing circuits, engineers can create a truth table for the desired output and then use Boolean Algebra to derive the corresponding logical expression. This process helps in confirming that the designed circuit will produce the correct output for all input scenarios, ensuring reliability in digital systems.
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