# NPTEL Digital System Design Week 3 Assignment Answers 2024

## 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’
`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
`Answer :- For Answer Click Here`

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’)
`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?

• 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 m11 )

• 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?

• C
• C’
• D’
• D
• 1
• 0
`Answer :- `

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

`Answer :- For Answer Click Here`