NPTEL Digital System Design Week 3 Assignment Answers 2024

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NPTEL Digital System Design Week 3 Assignment Answers 2024

1. Convert the expression (~A.B.~C)+(~A.B.C)+(A.~B.C) to POS form.

  • (~A+~B+~C).(~A+~B+C).(A+~B+C).(A+B+~C).(A+B+C)
  • (~A+~B+~C).(~A+~B+C).(A+~B+~C).(A+B+~C).(A+B+C)
  • (~A+~B+~C).(~A+~B+C).(~A+B+~C).(A+B+~C).(A+B+C)
  • (~A+~B+~C).(~A+~B+C).(A+~B+~C).(A+B+~C).(A+B+C)
Answer :- For Answer Click Here

2. What are the minterms for the given pos expression: (~A+~B+~C).(A+B+~C ).

  • [0, 2, 3, 4, 5, 6]
  • [6]
  • [1, 2, 3, 4, 5, 7]
  • [0, 6]
Answer :- For Answer Click Here

3. What is the simplified form of the expression boolean expression f=ab’+c+a’c’d+bc’d.

  • ab’+c+d
  • a’b’+c+d
  • ab+c’+d’
  • ad+c+d
Answer :- 

4. Given the boolean expression F = m+ m4 + m6 + m7, where m2, m4, m6, and m7 are the corresponding minterms to the input variables P, Q, and R, find the simplified sum of product expression for F.

  • PQ’ + QR’ + PR
  • P’Q + QR’ + PR’
  • PQ + QR’ + P’R’
  • PQ + QR’ + PR’
Answer :- For Answer Click Here

5. The minterm expansion of A’C’ + A’B +AB’C is

  • m0 + m2 + m3+m5
  • m0 + m1 + m6 +m7
  • m2 + m+ m4 +m5
  • m0 + m4 + m6 +m7
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6. What is the correct expression for F?

NPTEL Digital System Design Week 3 Assignment Answers 2024
  • F = (AB)’+(BC)+(AC’)
  • F = (AB)+(BC)+(AC)
  • F = ( A’B)+(BC)+(AC’)
  • F = (A’B).(BC).(AC’)
Answer :- For Answer Click Here

7. Which of the following Logic gates are also known as universal gates? (Multiple options may be correct)

  • AND
  • XNOR
  • OR
  • NAND
  • NOT
  • XOR
  • NOR
Answer :- 

8. What are the minterms for the given sop expression:
(~A.~B.~C)+(~A.~B.C)+(~A.B.~C)+(A.~B.C)+(A.B.~C)

  • [3,7,4]
  • [7]
  • [1,2,5,6]
  • [0,1,2,5,6]
  • None of the above
Answer :- 

9. Which of the following options are correct? (More than one may be correct)

  • (~C + (~A + ~B)) evaluates to 1 when A=0, B=0, C=0
  • ((~B + ~A) + ~(A.~A)) is always 1
  • F = m2 + m3 where are the corresponding minterms to the input A and B. Then F=(A+B).(~A+B)
  • The SOP form of (~A+~B).(A+~B).(A+B) is (~A.B)
Answer :- 

10. Minimize the given expression F = ΣΣ (1,5)

  • B’C + A’
  • B+A’
  • BC’+A
  • B’C
  • BC’
Answer :- For Answer Click Here

11. The given logic circuit represents?

NPTEL Digital System Design Week 3 Assignment Answers 2024
  • 4-bit binary to decimal converter
  • 4-bit decimal to excess-3 converter
  • 4-bit binary to gray code converter
  • 4-bit decimal to binary converter
Answer :- 

12. The following K-map represents Boolean function on 4 variables F(A,B,C,D) where X in the K map represents don’t care terms
Then which of the following options are correct?

NPTEL Digital System Design Week 3 Assignment Answers 2024
  • F = ΣΣ m(4, 9, 11, 13, 15) + ΣΣ d(2, 6)
  • F = ΣΣ m(2, 6, 11, 13, 15) + ΣΣ d(4, 6)
  • F = AD + A’BC’
  • F = AD + A’BD’
Answer :- 

13. Solve the following K-map and answer the following
(Note: Term AB’CD is minterm m11 )

NPTEL Digital System Design Week 3 Assignment Answers 2024
  • F = A’B’D’ + BCD + AB’
  • F = B’D’ + BCD + A’C’D’
  • F = ΠΠ (1, 3, 5, 6, 9, 11, 12, 13, 14)
  • F = ΠΠ (3, 4, 5, 6, 7, 9, 11, 12, 14)
Answer :- For Answer Click Here

14. How many SOP terms are there in the canonical SOP form of the following boolean function: F = ab + bc + cd + ad ? __________

Answer :- 

15. f1, f2, f3 are boolean functions over 4 variables A, B, C, D as follows

f1(A, B, C, D) = ΣΣ (0, 2, 4, 8, 10)
f2(A, B, C, D) = ΠΠ (2, 3, 4, 9, 11, 13, 15)f
3(A, B, C, D) = ΠΠ (1, 2, 4, 5, 7, 10)

Then what is the correct simplified form of F? 

NPTEL Digital System Design Week 3 Assignment Answers 2024
  • C
  • C’
  • D’
  • D
  • 1
  • 0
Answer :- 

16. Which of the following codes is used for labeling the cells of a K-map?

  • Hexadecimal
  • 8421 binary
  • BCD
  • Octal
  • Gray
Answer :- For Answer Click Here