## 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)

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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]

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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_{2 }+ m_{4} + m_{6} + m_{7}, where m_{2}, m_{4}, m_{6}, and m_{7} 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’

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

- m
_{0}+ m_{2}+ m_{3}+m_{5} - m
_{0}+ m_{1}+ m_{6}+m_{7} - m
_{2}+ m_{3 }+ m_{4}+m_{5} - m
_{0}+ m_{4}+ m_{6}+m_{7}

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6. What is the correct expression for F?

- F = (AB)’+(BC)+(AC’)
- F = (AB)+(BC)+(AC)
- F = ( A’B)+(BC)+(AC’)
- F = (A’B).(BC).(AC’)

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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 = m
_{2}+ m_{3}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’

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11. The given logic circuit represents?

- 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?

- 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 m_{11} )

- 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)

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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?

- 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

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