If (L)M(L)_M(L)M represents a number LLL in base-MMM number system, then…
2024
If (L)M(L)_M(L)M represents a number LLL in base-MMM number system, then identify the correct ascending order of the following numbers A–D when converted to decimal number system.
(A) (102)4
(B) (10001)2
(C) (103)6
(D) (201)3
Answer: D. (B), (A), (D), (C) — To solve this problem, convert each number from its given base to the decimal system. (A) (102)4 = 1 × 4² + 0 × 4¹ + 2 × 4⁰ = 16 + 0 + 2 = 18. (B) (10001)2 =…
- A.
(B), (A), (C), (D)
- B.
(A), (C), (D), (B)
- C.
(A), (B), (D), (C)
- D.
(B), (A), (D), (C)
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Correct answer: D
To solve this problem, convert each number from its given base to the decimal system.
(A) (102)4 = 1 × 4² + 0 × 4¹ + 2 × 4⁰ = 16 + 0 + 2 = 18. (B) (10001)2 = 1 × 2⁴ + 0 × 2³ + 0 × 2² + 0 × 2¹ + 1 × 2⁰ = 16 + 1 = 17. (C) (103)6 = 1 × 6² + 0 × 6¹ + 3 × 6⁰ = 36 + 0 + 3 = 39. (D) (201)3 = 2 × 3² + 0 × 3¹ + 1 × 3⁰ = 18 + 0 + 1 = 19.
Comparing the decimal values: 17 < 18 < 19 < 39. Thus, the ascending order is B, A, D, C.