NPTEL Digital System Design Week 3 Assignment Answers 2025
1. What is the correct logic gates representation for the simplified form of the following boolean expression
Y = A’C(A’BD)’+A’BC’D’+AB’C
- a
- b
- c
- d
- a,b
- c, d
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2. Simplify the following three variable expression Y(a,b,c) = ∑(0,1,3,4,7)
- a’b’ + bc + b’c’
- abc + a’b + bc
- a’b + bc + b’c’
- ab’ + bc + b’c’
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3. AB’.(ABC’ + A’B’C + AB’D + AB’C + AB’D’ + A’B’C’) simplifies to:
- AB’
- AB’C
- AB’D
- None of these
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4. Simplify the following boolean expression: A.(A+B’.C) + B’.(B’+C) + A’.B.C(A’.B’ + A’.B + A.B’.C + A.D)
- A.B.C
- A’.B.C
- (A’.B.C’)’
- AB + BC
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5. Expand A(B’+A)B to minterms
- ∑m(0,1,3,4)
- ∑m(3)
- ∑m(0,1)
- ∑m(0,1,2,3)
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6. The minterm expansion of f(A,B,C) = AB + BC’ + AC’ is
- ∑m (3, 4, 6, 7)
- ∑m (2, 4, 5, 7)
- ∑m (2, 4, 6,)
- ∑m (2, 4, 6, 7)
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7. simplify the following expressions using consensus theorem A’B’ + AC + BC’ + B’C + AB
- A’B’ + AC + BC’
- A’B + A’C + BC’
- A’B + AC + BC’
- A’B + AC + BC
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8. Express the following boolean function in POS form. F = A.B’ + B’.C
- ∏M (0,2,3,6)
- ∏M (0,2,3,6,7)
- ∏M (0,3,6,7)
- ∏M (2,3,6,7)
- ∏M (1,2,6,7)
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9. Express the following function into canonical form:
F = (X+Y+Z).(X+Y’).(Y+Z’)
- ∏(M0, M1, M2, M4, M5)
- ∏(M0, M2, M4, M3, M5)
- ∏(M0, M1, M2, M5, M6)
- ∏(M0, M1, M2, M3, M5)
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10. Simplify the following expression using consensus theorem
AC’+AB’D+A’B’C+A’CD’+B’C’D’
- AC’ + ACD’ + B’C’D’ + B’CD
- AC’ + A’CD’ + B’C’D’ + B’CD
- AC’ + A’CD’ + B’C’D’ + B’CD’
- AC’ + A’CD’ + B’C’D’ + B’C’D
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11. What is the minimum number of logic gates required to implement the following boolean expression: (A+B).(AB)’.
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12. what will be the minimum number of NAND gates required to implement the following boolean expression: A + AB’ + AB’C?
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13. How many 2-input NOR gates are required to implement F = (A’+B)(A+C+D)
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14. The following Kmap represents a Boolean function of 4 variables, which of the given options represents the minimal form of the Function?
- a’b’c’+abc+a’bd+ab’d
- a’b’c’d’+abcd+a’bd+ab’d
- a’b’c’d’+abcd+a’bd+abd’
- a’b’c’d’+abcd’+ab’d+a’bd
- None of the above
Answer :-
15. Minimize the K-map shown below and Identify the correct minimized boolean expression
- P’Q’+RS
- P’S’+RS
- P’S+RS’
- P’S+RS
- None of the above
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