Digital Circuits Week 3 Nptel Assignment Answers

Last updated: August 9, 2025

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Digital Circuits Week 3 Nptel Assignment Answers (July-Dec 2025)

Question 1. The Boolean function F(A,B,C) = ∑(3,4,6,7) is equivalent to

a) AB + BC’ + AC
b) A’B + BC + AC
c) AB + BC + AC’
d) AB + BC’ + AC’

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Question 2. Which of the following are prime implicants of the function F = ab’c’ + abc + a’bc + a’b’d’?
I) a’c d’
II) abcd
III) a’bc
IV) a’b’c’d

a) I and III only
b) II and IV only
c) None of the above
d) I and II only

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Question 3. Boolean expression can be minimized using ___________________

a) Algebraic Method
b) Demorgan’s Law
c) Karnaugh Map
d) Both a & c

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Question 4. The Boolean function F(A, B, C, D) = ∑ m(1, 3, 7, 11, 15) + ∑ d(0, 2, 9) is equivalent to

a) A̅C + BD
b) A̅D̅ + CD
c) A̅B̅ + CD
d) A̅D + B̅D

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Question 5. Simplify the Boolean Function F(W,X,Y,Z) = 𝛴 (0, 1, 2, 4, 5, 6, 8, 9, 12, 13, 14)

a) W + X + Y + Z
b) Y̅ + W̅Z̅ + XZ̅
c) Y + W̅Z̅ + XZ
d) X + W̅Z̅Y + X̅

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Question 6. The Boolean function F(A, B, C, D) = ∑ m(5, 7, 9, 10, 11) + ∑ d(0, 4,6, 8, 12, 14) is equivalent to

a) AB + A̅B̅
b) AB + C̅D
c) A̅B + AB̅
d) C̅D̅ + A̅B + AB̅

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Question 7. The SOP expression F = AB + CD is equivalent to the POS expression

a) (A + B)(C + D)
b) (A + C)(B + C)(A + D)(B + D)
c) (A + B)(C + D’)
d) (A + B)(C + D)(B + D)

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Question 8. Which type of logic circuit can directly implement the following Product-of-Sums (POS) expression without any conversion or transformation? Y = (A + B)(C + D + E)(F + G)

a) 2-level OR-AND logic circuit
b) 2-level AND-OR logic circuit
c) 2-level NAND logic circuit
d) 2-level NOR logic circuit

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Question 9. The POS expression F = (A’+B)(A’+C)(C+D) is equivalent to the SOP expression

a) AB + A’D + AC’
b) AC + A’D + BC’
c) A’C + A’D + BC
d) A’C + A’D + BC’

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Question 10. The minimized expression of the function F = X̅YZ + X̅Y Z̅ + XZ

a) X̅Z + YZ̅
b) X̅Y + XZ
c) X̅Y + YZ
d) XY + XZ

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Question 11. For an n-variable Boolean function, K-map contains how many cells or squares or cells?

a) n cells
b) 2n cells
c) 2ⁿ cells
d) 4n cells

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Question 12. The prime implicant which has at least one element that is not present in any other implicant is known as

a) Essential Prime Implicant
b) Non Implicant
c) Complement Implicant
d) Prime Complement

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Question 13. The reduced circuit of the following original circuit is

a) A
b) B
c) C
d) D

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Question 14. The Boolean function F(P,Q,R,S) = Σm(0,5,10,15) + d(2,7,8,13). Which of the following is the minimal SOP expression for F?

a) Q′S + QS′
b) Q′S′ + QS
c) Q′R′S′ + Q′RS′ + QR′S + QRS
d) P′Q′S′ + P′QS + PQS + PQ′S′

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Question 15. A combinational circuit has inputs A, B and C, and its K-Map is given. The output expression of the circuit is given by

a) (A̅B + AB̅)C
b) (A̅B + AB̅)C̅
c) A̅BC + AB̅C̅ + ABC̅ + A̅B̅C̅
d) A̅B̅C̅ + ABC + A̅BC̅ + AB̅C̅

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Digital Circuits Week 3 Nptel Assignment Answers (July-Dec 2024)

Session: JULY – DEC 2024

Q1. How many cells or squares K-map contains for an n-variable Boolean function?
A) n cells
B) 2n cells
C) 2ª cells
D) 22n cells

Answer: C) 2ª cells

Q2. The prime implicant which has at least one element that is not present in any other implicant is known as
A) Essential Prime Implicant
B) Non Implicant
C) Complement Implicant
D) Prime Complement

Answer: A) Essential Prime Implicant

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