If (L)M represents a number L in base-M number system, then which of the…
2024
If (L)M represents a number L in base-M number system, then which of the following numbers are equivalent to (19)16?
(A) (11001)2 (B) (201)3 (C) (121)4 (D) (101)5 (E) (25)10
Choose the correct answer from the options given below :
Answer: A. (A), (C) and (E) Only — First, convert (19)₁₆ to decimal: 1 × 16 + 9 = 25. Next, evaluate each option: (A) (11001)₂ = 16 + 8 + 1 = 25. (B) (201)₃ = 18 + 1 = 19. (C) (121)₄ = 16 + 8 +…
- A.
(A), (C) and (E) Only
- B.
(B) and (D) Only
- C.
(A), (B) and (D) Only
- D.
(A), (B), (C), (D) and (E)
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Show answer & explanation
Correct answer: A
First, convert (19)₁₆ to decimal: 1 × 16 + 9 = 25. Next, evaluate each option: (A) (11001)₂ = 16 + 8 + 1 = 25. (B) (201)₃ = 18 + 1 = 19. (C) (121)₄ = 16 + 8 + 1 = 25. (D) (101)₅ = 25 + 1 = 26. (E) (25)₁₀ = 25. Thus, options A, C, and E are equivalent to (19)₁₆.