## NPTEL Computer Architecture Week 7 Assignment Answers 2024

1. The result of the following addition is *_________*.

(1101.101)_{2} + (1011.11)_{2}

- (11001.111)
_{2} - (11001.011)
_{2} - (11000.011)
_{2} - (1001.011)
_{2}

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2. The expression for Cout of a full adder is *___________*.

- C
_{out}= a.b - C
_{out}= a.b + a.c_{in}+ b.c_{in} - C
_{out}= a.b.c_{in} - C
_{out}= a’.b + a’. C_{in}+ b.c_{in}

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3. Consider a function f(n) = 2^{12}n^{55} + 2^{4}n^{28} + 32. What is its asymptotic time complexity?

- f(n) = O(n
^{28}) - f(n) = O(n
^{55}) - f(n) = O(n
^{83}) - f(n) = O(1)

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4. The total time complexity of the carry-select adder for performing an n-bit addition is *___________*.

- O(n)
- O(sqrt(n))
- O(log n)
- O(n log n)

Answer :-

5. In a Booth multiplier, if the bit pair consisting of the current and the previous multiplier bit is (0,1) then we need to __________.

- Subtract the multiplicand
- Add the multiplicand
- Subtract the multiplier
- Do nothing

Answer :-

6. Consider a carry lookahead adder, let the inputs be A_{i} = 1, B_{i} = 0 and the carry input C_{in} = 1. What are the values of gi, p_{i} and C_{out}?

- g
_{i}= 1, p_{i}= 1 and C_{out}= 0 - g
_{i }= 0, p_{i}= 0 and C_{out}= 0 - g
_{i}= 0, p_{i}= 1 and C_{out}= 1 - g
_{i}= 1, p_{i}= 1 and C_{out}= 1

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7. In a ripple carry adder circuit for adding two 8-bit numbers, we need to have **_ full adders and _** half adder(s)?

- 7, 1
- 0, 8
- 2, 6
- 6, 2

Answer :-

8. The Wallace tree multiplier uses a ______________ in the last stage.

- Ripple Carry Adder
- Carry Select Adder
- Carry Lookahead Adder
- Carry Save Adder

Answer :-

9. How many levels are there in a Wallace tree multiplier?

- log
_{3/2}(n) - n/2
- log
_{3/2}(n) + 1 - n
^{2}

Answer :-

10. Select the correct statement/s. Choose the most appropriate option.

- The asymptotic time complexity of the Wallace tree multiplier is O(log(n)).
- The Booth multiplier takes advantage of a continuous run of 1s to speed up the multiplication process.
- In a carry select adder, sqrt(n) is the optimal block size for adding two n-bit numbers.
- All of the options

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