If (L)M represents a number L in the base-M number system, identify the…
2024
If (L)M represents a number L in the base-M number system, identify the correct descending order of the following numbers A–D after converting them to decimal:
A. (123)7
B. (1211)3
C. (212)6
D. (201)5
Choose the most appropriate answer from the options given below.
Answer: D. C, A, D, B — ConceptIn a positional base-b numeral, each digit has a place value determined by a power of b. Starting from the rightmost digit at power 0, the decimal…
- A.
A, C, B, D
- B.
B, D, A, C
- C.
D, B, C, A
- D.
C, A, D, B
Attempted by 3 students.
Show answer & explanation
Correct answer: D
Concept
In a positional base-b numeral, each digit has a place value determined by a power of b.
Starting from the rightmost digit at power 0, the decimal value is the sum of each digit multiplied by its corresponding power of the base. Convert every numeral to the same base before comparing them.
Application
A: (123)7 = 1 × 72 + 2 × 7 + 3 = 49 + 14 + 3 = 66.
B: (1211)3 = 1 × 33 + 2 × 32 + 1 × 3 + 1 = 27 + 18 + 3 + 1 = 49.
C: (212)6 = 2 × 62 + 1 × 6 + 2 = 72 + 6 + 2 = 80.
D: (201)5 = 2 × 52 + 0 × 5 + 1 = 50 + 0 + 1 = 51.
Cross-check
The adjacent comparisons 80 > 66, 66 > 51, and 51 > 49 are all true, confirming one strictly descending sequence.
Result
Therefore, C = 80 > A = 66 > D = 51 > B = 49, so the descending order is C, A, D, B.