Digital Logic Circuits and Discrete Mathematical Structures Topic Wise Pyq

41. Number of combinations of two 8-bit numbers:
दो 8-bit numbers के combinations कितने होंगे?
(LT Grade C.S. 2018)
A. 2⁹
B. 2⁸
C. 2¹⁶
D. 2⁴

Correct Answer: C

Explanation (EN): Each number has 2⁸ values Total combinations = 2⁸ × 2⁸ = 2¹⁶

Explanation (HI): हर 8-bit संख्या के 2⁸ मान होते हैं कुल combinations = 2¹⁶

42. Binary equivalent of Gray code 11100:
Gray code 11100 का binary equivalent क्या है?
(LT Grade C.S. 2018)
A. 10111
B. 00111
C. 01011
D. 10101

Correct Answer: A

Explanation (EN): MSB same = 1 Then XOR step-by-step → result = 10111

Explanation (HI): पहला bit same रहता है बाकी XOR करने पर उत्तर = 10111

43. Decimal value of 1011.1101₂:
1011.1101₂ का decimal equivalent क्या है?
(BPSC TRE 2024)
A. 11.75
B. 12.125
C. 13.5
D. More than one

Correct Answer: E

Explanation (EN): Integer = 11 Fraction = 0.8125 Total = 11.8125 → none matches

Explanation (HI): पूर्णांक = 11 भिन्न = 0.8125 कुल = 11.8125 → कोई विकल्प सही नहीं

44. Convert 1234₁₀ into binary, octal and hexadecimal:
1234₁₀ का binary, octal और hexadecimal रूप क्या है?
(BPSC TRE 2024)
A. 10011010010, 2322, 4D2
B. 11001110010, 1712, 72A
C. 11100110010, 1642, 3CD
D. More than one

Correct Answer: A

Explanation (EN): 1234₁₀ → binary = 10011010010 octal = 2322 hex = 4D2

Explanation (HI): 1234 का रूपांतरण: Binary = 10011010010 Octal = 2322 Hex = 4D2

45. (651.124)₈ = ?
(651.124)₈ का hexadecimal equivalent क्या है?
(BPSC TRE 2024)
A. (1A9.2A)₁₆
B. (1B0.10)₁₆
C. (1A8.A3)₁₆
D. More than one

Correct Answer: A

Explanation (EN): Convert octal → binary → hex → result = 1A9.2A

Explanation (HI): Octal को binary और फिर hex में बदलने पर उत्तर = 1A9.2A

46. Range of n-bit sign magnitude representation:
n-bit sign magnitude representation की range क्या है?
(RPSC C.S. 2016)
A. –(2ⁿ–1) to +(2ⁿ–1)
B. –(2ⁿ⁻¹–1) to +(2ⁿ⁻¹–1)
C. –2ⁿ to +(2ⁿ–1)
D. –2ⁿ⁻¹ to +(2ⁿ–1)

Correct Answer: B

Explanation (EN): Sign bit = 1 Magnitude bits = n–1 Range = –(2ⁿ⁻¹–1) to +(2ⁿ⁻¹–1)

Explanation (HI): 1 bit sign के लिए और बाकी magnitude के लिए Range = –(2ⁿ⁻¹–1) से +(2ⁿ⁻¹–1)

47. Result of +3 and –4 in 4-bit 2’s complement:
4-bit 2’s complement में +3 और –4 का योग क्या होगा?
(RPSC C.S. 2016)
A. 1001
B. 1010
C. 1100
D. 1111

Correct Answer: D

Explanation (EN): +3 = 0011 –4 = 1100 Add → 1111 = –1

Explanation (HI): +3 = 0011 –4 = 1100 योग = 1111 (–1)

48. IEEE 754 value of given binary:
दिए गए IEEE 754 binary का मान क्या है?
(RPSC C.S. 2016)
A. 3.5
B. –3.5
C. 4.8
D. –4.8

Correct Answer: A

Explanation (EN): Sign = 0 → positive Exponent = 1 Mantissa = 1.75 Final value = 3.5

Explanation (HI): Sign = positive Exponent = 1 Mantissa = 1.75 अंतिम मान = 3.5

49. Find base b:
(142)b + (112)b-2 = (75)₈ में base b क्या है?
(UGC NET 2019)
A. 3
B. 6
C. 7
D. 5

Correct Answer: D

Explanation (EN): After solving equation → b = 5

Explanation (HI): समीकरण हल करने पर b = 5

50. Which codes are self-complementing?
कौन-से code self-complementing हैं?
(UGC NET 2019)
A. 8421 & 2421
B. 2421 & Excess-3
C. Excess-3 & Gray
D. Gray & 8421

Correct Answer: B

Explanation (EN): Self-complementing codes: • 2421 • Excess-3

Explanation (HI): Self-complementing code होते हैं: • 2421 • Excess-3

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