Digital Logic Circuits and Discrete Mathematical Structures Topic Wise Pyq

91. Excess-3 decimal code is self-complementing because:
Excess-3 decimal code self-complementing क्यों है?
(UGC NET C.S. December-2014 Paper-II)
A. -1
B. (2) and (3)
C. (1) and (3)
D. All are correct

Correct Answer: C

Explanation (EN): Excess-3 is self-complementing because: 1. The binary sum of a code and its 9's complement corresponds correctly. 2. Its complement can be generated by inverting each bit pattern. So statements (1) and (3) are correct.

Explanation (HI): Excess-3 code self-complementing होता है क्योंकि: 1. किसी code और उसके 9's complement का संबंध सही प्रकार से बनता है। 2. केवल bit inversion से उसका complement प्राप्त किया जा सकता है। इसलिए सही उत्तर (1) और (3) है।

92. For the 8-bit word 00111001, if stored check bits are 0111 and recalculated check bits are 1101, what data word was read?
यदि 8-bit word 00111001 के साथ stored check bits 0111 हैं और पढ़ने पर check bits 1101 मिलते हैं, तो read data word क्या था?
(UGC NET C.S. June-2015 Paper-III)
A. 10011001
B. 00011001
C. 00111000
D. 11000110

Correct Answer: B

Explanation (EN): Given stored check bits = 0111 Calculated check bits = 1101 XOR them: 0111 XOR 1101 = 1010 1010₂ = 10, so error is at position 10. That corresponds to bit d6, so flip that bit in the original data word. Thus the read data word becomes 00011001

Explanation (HI): Stored check bits = 0111 Calculated check bits = 1101 अब XOR करें: 0111 XOR 1101 = 1010 1010₂ = 10, अतः error position 10 है। यह d6 bit को दर्शाता है, इसलिए उसे flip करेंगे। इससे read data word 00011001 मिलेगा।

93. Hexadecimal equivalent of octal number 2550276 is:
Octal संख्या 2550276 का hexadecimal equivalent क्या है?
(UGC NET C.S. June-2015 Paper-III)
A. FADED
B. AE0BE
C. AD0BE
D. ACABE

Correct Answer: C

Explanation (EN): Convert octal to binary: 2550276₈ = 010 101 101 000 010 111 110 Now group in 4 bits: 0000 1010 1101 0000 1011 1110 This gives hexadecimal: 0 A D 0 B E So answer = AD0BE

Explanation (HI): Octal को binary में बदलें: 2550276₈ = 010 101 101 000 010 111 110 अब 4-4 bits के समूह बनाएं: 0000 1010 1101 0000 1011 1110 इससे hexadecimal मिलेगा: 0 A D 0 B E अतः उत्तर = AD0BE

94. Convert octal number 0.4051 to decimal.
Octal संख्या 0.4051 को decimal में बदलिए।
(UGC NET C.S. June-2017 Paper-II)
A. 0.5100098
B. 0.2096
C. 0.52
D. 0.4192

Correct Answer: A

Explanation (EN): 0.4051₈ = 4×8⁻¹ + 0×8⁻² + 5×8⁻³ + 1×8⁻⁴ = 4×(1/8) + 0 + 5×(1/512) + 1×(1/4096) = 0.5 + 0 + 0.009765625 + 0.000244140625 = 0.510009765625 Approximate value = 0.5100098

Explanation (HI): 0.4051₈ = 4×8⁻¹ + 0×8⁻² + 5×8⁻³ + 1×8⁻⁴ = 4×(1/8) + 0 + 5×(1/512) + 1×(1/4096) = 0.5 + 0 + 0.009765625 + 0.000244140625 = 0.510009765625 लगभग मान = 0.5100098

95. Hexadecimal equivalent of octal number 2357 is:
Octal संख्या 2357 का hexadecimal equivalent क्या है?
(UGC NET C.S. June-2017 Paper-II)
A. 2EE
B. 2FF
C. 4EF
D. 4FE

Correct Answer: C

Explanation (EN): Convert octal to binary: 2 = 010 3 = 011 5 = 101 7 = 111 So binary = 010011101111 Group into 4 bits: 0100 1110 1111 = 4 E F Hence answer = 4EF

Explanation (HI): Octal को binary में बदलें: 2 = 010 3 = 011 5 = 101 7 = 111 इसलिए binary = 010011101111 अब 4-4 bits के समूह बनाएं: 0100 1110 1111 = 4 E F अतः उत्तर = 4EF

96. Octal equivalent of binary number 1011101011 is:
Binary संख्या 1011101011 का octal equivalent क्या है?
(UGC NET C.S. November-2017 Paper-II)
A. 7353
B. 1353
C. 5651
D. 5657

Correct Answer: B

Explanation (EN): Group the binary digits into 3 from right: 1011101011 → 001 011 101 011 Now convert each group: 001 = 1 011 = 3 101 = 5 011 = 3 So octal = 1353

Explanation (HI): दाईं ओर से 3-3 bits के समूह बनाएं: 1011101011 → 001 011 101 011 अब प्रत्येक समूह को octal में बदलें: 001 = 1 011 = 3 101 = 5 011 = 3 अतः octal रूप = 1353

97. Let m = (313)₄ and n = (322)₄. Find base-4 expansion of m + n.
यदि m = (313)₄ और n = (322)₄, तो m + n का base-4 विस्तार ज्ञात कीजिए।
(UGC NET C.S. November-2017 Paper-II)
A. (635)₄
B. (32312)₄
C. (21323)₄
D. (1301)₄

Correct Answer: D

Explanation (EN): Convert (313)₄ to decimal: = 3×4² + 1×4 + 3 = 48 + 4 + 3 = 55 Convert (322)₄ to decimal: = 3×4² + 2×4 + 2 = 48 + 8 + 2 = 58 Now add: 55 + 58 = 113 Convert 113 to base 4: 113 = 1301₄

Explanation (HI): (313)₄ को decimal में बदलें: = 55 (322)₄ को decimal में बदलें: = 58 अब जोड़ें: 55 + 58 = 113 113 का base-4 रूप = 1301₄

98. Identify the code sequence: 1010 1011 1001 1000
Code sequence 1010 1011 1001 1000 की पहचान कीजिए।
(UGC NET C.S. December-2023)
A. BCD
B. Excess-3
C. Gray
D. Excess-3 Gray

Correct Answer: C

Explanation (EN): This sequence matches the pattern of Gray code, where adjacent values differ by only one bit.

Explanation (HI): यह क्रम Gray code के pattern से मेल खाता है, जिसमें लगातार मानों में केवल 1 bit का अंतर होता है।

99. What is the (4+4) bit binary fixed-point equivalent of −(3.72)₁₀ ?
−(3.72)₁₀ का (4+4) bit binary fixed-point equivalent क्या है?
(UGC NET C.S. June-2023)
A. 0011.1100
B. 0011.1010
C. 1100.01
D. 0011.1011

Correct Answer: C

Explanation (EN): For integer part: 3 in binary = 0011 In 4-bit 2's complement, −3 is represented as 1100 For fractional part 0.72, repeated multiplication gives binary approximation. In fixed-point 4-bit fraction, it is taken as 0100. So final fixed-point representation = 1100.0100

Explanation (HI): पूर्णांक भाग के लिए: 3 का binary = 0011 4-bit 2's complement में −3 का रूप = 1100 भिन्न भाग 0.72 को binary fixed-point में लगभग 0100 लिया जाता है। इसलिए अंतिम उत्तर = 1100.0100

100. In 16-bit 2's complement representation, decimal number 28 is:
16-bit 2's complement representation में decimal संख्या 28 का रूप क्या होगा?
(UGC NET C.S. December-2022)
A. 1111 1111 0001 1100
B. 1111 1111 1111 0100
C. 1111 1111 1110 0100
D. 1111 1111 1110 0011

Correct Answer: C

Explanation (EN): The options show the 2's complement form of −28. First write +28 in binary: 28 = 0000 0000 0001 1100 Now take 1's complement: 1111 1111 1110 0011 Add 1: 1111 1111 1110 0100 So the correct representation is 1111 1111 1110 0100

Explanation (HI): यहाँ विकल्प वास्तव में −28 का 2's complement रूप दिखा रहे हैं। पहले +28 को binary में लिखें: 28 = 0000 0000 0001 1100 अब 1's complement लें: 1111 1111 1110 0011 अब 1 जोड़ें: 1111 1111 1110 0100 अतः सही उत्तर 1111 1111 1110 0100 है।