Which of the following statement(s) is/are correct? I. (4052)₇ = (1409)₁₀ II.…
2021
Which of the following statement(s) is/are correct? I. (4052)₇ = (1409)₁₀ II. (1715)₁₀ = (BAB)₁₂
- A.
Only I
- B.
Only II
- C.
Both I and II
- D.
Neither I nor II
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Correct answer: C
Step 1: Convert (4052)₇ to base 10. Use the formula: 4×7³ + 0×7² + 5×7¹ + 2×7⁰. Calculate: 4×343 = 1372, 0×49 = 0, 5×7 = 35, 2×1 = 2. Sum: 1372 + 0 + 35 + 2 = 1409. So, (4052)₇ = (1409)₁₀. This statement is correct.
Step 2: Convert (1715)₁₀ to base 12. Divide 1715 by 12: 1715 ÷ 12 = 142 remainder 11 (B). 142 ÷ 12 = 11 remainder 10 (A). 11 ÷ 12 = 0 remainder 11 (B). Reading remainders from bottom to top gives (BAB)₁₂. This statement is correct.
Both statements are correct. Therefore, the correct option is C.