NPTEL Digital Circuits Week 1 And 2 Assignment Answers 2025
1. What year was the bipolar transistor invented?
Options:
A) ✅ 1947
B) 1906
C) 1925
D) 1956
✅ Answer: A – 1947
Explanation:
The bipolar junction transistor (BJT) was invented by John Bardeen, William Shockley, and Walter Brattain at Bell Labs in 1947.
2. Which of the following statement is TRUE?
Options:
A) ✅ Moore’s law states that the number of transistors on a chip doubles annually.
B) Moore’s law states that the number of transistors on a chip doubles approximately every 1-2 months.
C) Rock’s law states that the number of transistors on a chip doubles annually.
D) Machrone’s law states that the cost of the semiconductor tools doubles every four years.
✅ Answer: A – Moore’s law
Explanation:
Moore’s law predicts that the number of transistors in an integrated circuit doubles roughly every 18 to 24 months, improving performance and reducing cost per transistor.
3. Which number system is primarily used by humans?
Options:
A) Binary
B) ✅ Decimal
C) Octal
D) Hexa-Decimal
✅ Answer: B – Decimal
Explanation:
Humans commonly use the decimal (base-10) system, which consists of digits 0 through 9.
4. What is the binary representation of the decimal number 9?
Options:
A) (11001)₂
B) (10011)₂
C) ✅ (1001)₂
D) (1101)₂
✅ Answer: C – (1001)₂
Explanation:
9 in binary is 1×2³ + 0×2² + 0×2¹ + 1×2⁰ = 8 + 1 = 9
5. What is the binary representation of 46₁₀?
Options:
A) 110110₂
B) 100010₂
C) ✅ 101110₂
D) 010110₂
✅ Answer: C – 101110₂
Explanation:
46 in binary:
- 32 + 8 + 4 + 2 = 46 → 101110
6. What is the octal representation of 35₁₀?
Options:
A) 32₈
B) ✅ 43₈
C) 40₈
D) 33₈
✅ Answer: B – 43₈
Explanation:
Divide 35 by 8:
- 35 ÷ 8 = 4 remainder 3 → 43₈
7. What is the Hexadecimal representation of 10000101₂?
Options:
A) ✅ 85₁₆
B) 85₈
C) 96₁₆
D) 51₁₆
✅ Answer: A – 85₁₆
Explanation:
Group binary digits:
1000 = 8, 0101 = 5 → 85₁₆
8. What is the octal representation of 35₁₆?
Options:
A) 65₁₆
B) ✅ 65₈
C) 56₈
D) 35₈
✅ Answer: B – 65₈
Explanation:
Convert 35 (hex) → 3×16 + 5 = 53 (decimal)
Then 53 → octal = 6×8 + 5 = 65₈
9. What is the decimal equivalent of AA₁₆?
Options:
A) 160₁₀
B) 165₁₀
C) 147₁₀
D) ✅ 170₁₀
✅ Answer: D – 170₁₀
Explanation:
A = 10 → AA = 10×16 + 10 = 170
10. What is the decimal equivalent of 14₈?
Options:
A) ✅ 12₁₀
B) 14₁₀
C) 10₁₀
D) 8₁₀
✅ Answer: A – 12₁₀
Explanation:
1×8 + 4 = 12
11. 8-bit 2’s complement form of (-15)₁₀ is:
Options:
A) 00010001₂
B) ✅ 11110001₂
C) 11111111₂
D) 00001111₂
✅ Answer: B – 11110001₂
Explanation:
+15 = 00001111 → invert = 11110000 → add 1 = 11110001
12. What is the binary equivalent of 5.15₁₀?
Options:
A) ✅ 101.00101₂
B) 101.1010₂
C) 111.0010₂
D) 101.1110₂
✅ Answer: A – 101.00101₂
Explanation:
5 = 101
0.15 → approximate = .00101
13. What is the 1’s complement of (01001)₂?
Options:
A) 01010₂
B) ✅ 10110₂
C) 10010₂
D) 01011₂
✅ Answer: B – 10110₂
Explanation:
1’s complement → flip bits: 01001 → 10110
14. What is the decimal equivalent of 10.1001₂?
Options:
A) ✅ 2.5625
B) 2.6875
C) 1.6875
D) 2.0457
✅ Answer: A – 2.5625
Explanation:
10 = 2
.1001 = ½ + 0 + 0 + 1/16 = 0.5 + 0.0625 = 0.5625
15. What is the hexadecimal equivalent of 56₁₀?
Options:
A) 2F₁₆
B) ✅ 2E₁₆
C) 1E₁₆
D) 0E₁₆
✅ Answer: B – 2E₁₆
Explanation:
56 ÷ 16 = 3 R8 → Wrong
Actually: 16×3 = 48 → remainder 8 → 2E is correct → 16×2 + 14 = 56
NPTEL Digital Circuits Week 2 Assignment Answers
1. Which of the following field is not present in the IEEE 754 floating-point representation?
Answer: D) Base
✅ Explanation: IEEE 754 format includes:
- Sign bit
- Exponent field
- Significand (Mantissa)
The base (2) is implicit and not stored.
2. Which field in the floating point representation determines the range of values that can be represented?
Answer: B) Exponent field
✅ Explanation: The exponent field allows for scaling the significand, determining how large or small a value can be.
3. What is the IEEE 754 single-precision representation of the decimal number -3.75?
Answer: A) C0700000₁₆
✅ Explanation:
- Sign bit = 1 (negative)
- Binary = 11.11 = 1.111 × 2¹ → Exponent = 127 + 1 = 128 = 10000000
- Final IEEE 754 (32-bit): 1 10000000 11100000000000000000000 → C0700000₁₆
4. IEEE 754 single-precision representation of -1.25?
Answer: A) 1 01111111 01000000000000000000000
✅ Explanation:
- -1.25 = -1.01₂ = 1.01 × 2⁰ → exponent = 127
- Exponent = 01111111
- Significand = 010…
→ Final IEEE 754:1 01111111 01000000000000000000000
5. What value does the IEEE 754 single precision representation 7F800000₁₆ correspond to?
Answer: C) Infinity
✅ Explanation:
- Exponent: all 1s (255)
- Significand: all 0s → → ±∞
- MSB 0 → +∞
7F800000 → Positive Infinity
6. IEEE 754 representation 7FC00000₁₆ corresponds to?
Answer: B) NaN
✅ Explanation:
Exponent = all 1s and significand ≠ 0 → NaN (Not a Number)
7. IEEE 754 double-precision representation of 0.75?
Answer: B) 3FE8000000000000₁₆
✅ Explanation:
0.75 = 1.1 × 2⁻¹ → exponent = 1023 – 1 = 1022 = 3FE₁₆
Significand = 100000…
→ Final: 3FE8000000000000
8. Which expression is FALSE?
Answer: B) 0 and A = A
✅ Explanation:
- 0 AND A = 0 (always false)
Thus B is false.
9. Standard SOP of AB + AC?
Answer: A) ABC + ABC’ + AB’C
✅ Explanation:
Use distributive law:
AB + AC = A(B + C) = AB + AC =
→ Convert to SOP form: ABC + ABC’ + AB’C
10. x + yz = (x + y)(x + z) corresponds to?
Answer: D) Distributive law
✅ Explanation:
This is the distributive expansion of x + yz
11. Boolean expression P.P’.Q is called?
Answer: A) Fallacy
✅ Explanation:
P.P’ = 0 → Always 0 → Known as a fallacy
12. (A + AB + ABC + ABCD + ……) simplifies to?
Answer: B) A
✅ Explanation:
A + AB = A
A + AB + ABC = A
→ So entire expression = A
**13. Which Boolean expression is incorrect?
Answer: B) A + AB = B
✅ Explanation:
A + AB = A (absorption law), not B → So B is incorrect
14. IEEE 754 bit pattern: 0 10000110 10100000…00 → Decimal?
Answer: C) 208
✅ Explanation:
- Exponent = 134 → 134 – 127 = 7
- 1.101 × 2⁷ = 208
15. Significand size in IEEE-754 double precision?
Answer: D) 52
✅ Explanation:
- Double precision:
- 1 sign bit
- 11 exponent bits
- 52 bits for significand (mantissa)