If (L)M represents L written in base M, identify the correct ascending order…
2024
If (L)M represents L written in base M, identify the correct ascending order of A-D after conversion to decimal:
A. (11111.11)2
B. (102.3)6
C. (42.5)8
D. (32.6)16
Choose the most appropriate answer from the options below:
Answer: B. A, C, B, D — Concept: In a positional base-b numeral, each digit is multiplied by b raised to its place value. Positions to the left of the radix point use non-negative…
- A.
B, A, C, D
- B.
A, C, B, D
- C.
C, A, D, B
- D.
D, C, B, A
Attempted by 10 students.
Show answer & explanation
Correct answer: B
Concept: In a positional base-b numeral, each digit is multiplied by b raised to its place value.
Positions to the left of the radix point use non-negative powers of b; positions to the right use negative powers of b.
Application: Convert each numeral to decimal by expanding its digits by place value:
A: (11111.11)2 = 1×24 + 1×23 + 1×22 + 1×21 + 1×20 + 1×2-1 + 1×2-2 = 31.75.
B: (102.3)6 = 1×62 + 0×61 + 2×60 + 3×6-1 = 38.5.
C: (42.5)8 = 4×81 + 2×80 + 5×8-1 = 34.625.
D: (32.6)16 = 3×161 + 2×160 + 6×16-1 = 50.375.
Cross-check: The decimal values lie on one common scale; the table makes their relative sizes explicit.
Numeral | Decimal value |
|---|---|
A | 31.75 |
C | 34.625 |
B | 38.5 |
D | 50.375 |
Result: Therefore, the ascending order is A, C, B, D.