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If in base-M number system, (L)M represents the number L, then identify the correct ascending order of the following numbers A-D when converted into decimal number system:

A. (203)4
B. (100001)2
C. (114)5
D. (1012)3

1. D, B, C, A
2. B, D, C, A
3. A, B, C, D
4. D, B, A, C

यदि आधार-M संख्या प्रणाली में, (L)M संख्या L को दर्शाता है, तो निम्न संख्याओं A-D को दशमलव संख्या प्रणाली में परिवर्तित करने पर उनके सही आरोही क्रम की पहचान कीजिए :

A. (203)4
B. (100001)2
C. (114)5
D. (1012)3

1. D, B, C, A
2. B, D, C, A
3. A, B, C, D
4. D, B, A, C

This Question came in

UGC-NET-Hindi-27-August-2024-Shift-2-Q42

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Detailed Explanation & Answer

A. (203)₄ (Base 4):
2 × 4^2 + 0 × 4^1 + 3 × 4^0 = 2 × 16 + 0 + 3 = 32 + 3 = 35

B. (100001)₂ (Base 2):
1 × 2^5 + 0 × 2^4 + 0 × 2^3 + 0 × 2^2 + 0 × 2^1 + 1 × 2^0 = 1 × 32 + 0 + 0 + 0 + 0 + 1 = 32 + 1 = 33

C. (114)₅ (Base 5):
1 × 5^2 + 1 × 5^1 + 4 × 5^0 = 1 × 25 + 1 × 5 + 4 = 25 + 5 + 4 = 34

D. (1012)₃ (Base 3):
1 × 3^3 + 0 × 3^2 + 1 × 3^1 + 2 × 3^0 = 1 × 27 + 0 + 1 × 3 + 2 = 27 + 0 + 3 + 2 = 32

ए. (203)₄ (बेस 4):
2 × 4^2 + 0 × 4^1 + 3 × 4^0 = 2 × 16 + 0 + 3 = 32 + 3 = 35

बी. (100001)₂ (बेस 2):
1 × 2^5 + 0 × 2^4 + 0 × 2^3 + 0 × 2^2 + 0 × 2^1 + 1 × 2^0 = 1 × 32 + 0 + 0 + 0 + 0 + 1 = 32 + 1 = 33

सी. (114)₅ (बेस 5):
1 × 5^2 + 1 × 5^1 + 4 × 5^0 = 1 × 25 + 1 × 5 + 4 = 25 + 5 + 4 = 34

डी. (1012)₃ (बेस 3):
1 × 3^3 + 0 × 3^2 + 1 × 3^1 + 2 × 3^0 = 1 × 27 + 0 + 1 × 3 + 2 = 27 + 0 + 3 + 2 = 32

The Correct Answer is 1

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