If (L) in base M represents the number L written in the base-M number system,…
2024
If (L) in base M represents the number L written in the base-M number system, identify the ascending order of the following numbers after converting them to decimal:
A. (203)4
B. (100001)2
C. (114)5
D. (1012)3
Choose the correct answer from the options given below.
Answer: A. D, B, C, A — ConceptIn a positional numeral system with base b, a numeral (dn…d1d0) has decimal value dnbn + … + d1b + d0. Each digit is multiplied by the power of the…
- A.
D, B, C, A
- B.
B, D, C, A
- C.
A, B, C, D
- D.
D, B, A, C
Attempted by 12 students.
Show answer & explanation
Correct answer: A
Concept
In a positional numeral system with base b, a numeral (dn…d1d0) has decimal value dnbn + … + d1b + d0.
Each digit is multiplied by the power of the base determined by its position, counting from 0 at the rightmost digit.
Application
A = (203)4 = 2 × 42 + 0 × 41 + 3 × 40 = 32 + 0 + 3 = 35
B = (100001)2 = 1 × 25 + 1 × 20 = 32 + 1 = 33
C = (114)5 = 1 × 52 + 1 × 51 + 4 × 50 = 25 + 5 + 4 = 34
D = (1012)3 = 1 × 33 + 1 × 31 + 2 × 30 = 27 + 3 + 2 = 32
Cross-check
Label | Decimal value |
|---|---|
D | 32 |
B | 33 |
C | 34 |
A | 35 |
The values are consecutive integers, so the ascending order is D, B, C, A.