If (L)M represents a number L in base-M number system, then identify the…
2024
If (L)M represents a number L in base-M number system, then identify the correct descending order of the following numbers A-D, when converted to base-10 (decimal) number system.
(A) (9C)16 (B) (233)8 (C) (313)7 (D) (10011110)2
Choose the correct answer from the options given below :
- A.
(C), (D), (B), (A)
- B.
(D), (C), (A), (B)
- C.
(B), (C), (A), (D)
- D.
(D), (C), (B), (A)
Attempted by 43 students.
Show answer & explanation
Correct answer: B
First, convert each number to base-10 (decimal).
A = (9C)₁₆ = 9×16 + 12 = 156.
B = (233)₈ = 2×8² + 3×8 + 3 = 155.
C = (313)₇ = 3×7² + 1×7 + 3 = 157.
D = (10011110)₂ = 128 + 16 + 8 + 4 + 2 = 158.
Arranging in descending order: D (158) > C (157) > A (156) > B (155).
Thus, the correct order is D, C, A, B.