If (L)M represent a number L in base-M number system, then identify the…
2026
If (L)M represent a number L in base-M number system, then identify the correct descending order of the following numbers A-D when converted to decimal number system.
A. (30002.2)4
B. (100000.11)2
C. (666.2)8
D. (D5.6)16
Choose the correct answer from the options given below:
- A.
A, C, D, B
- B.
B, C, D, A
- C.
C, A, B, D
- D.
D, B, A, C
Attempted by 68 students.
Show answer & explanation
Correct answer: A
To determine the correct descending order, we first convert each number from its given base to the decimal (base-10) system.
A. (30002.2)₄ = 3×4⁴ + 0×4³ + 0×4² + 0×4¹ + 2×4⁰ + 2×4⁻¹ = 768 + 0 + 0 + 0 + 2 + 0.5 = 770.5
B. (100000.11)₂ = 1×2⁵ + 0×2⁴ + ... + 1×2⁻¹ + 1×2⁻² = 32 + 0.5 + 0.25 = 32.75
C. (666.2)₈ = 6×8² + 6×8¹ + 6×8⁰ + 2×8⁻¹ = 384 + 48 + 6 + 0.25 = 438.25
D. (D5.6)₁₆ = 13×16¹ + 5×16⁰ + 6×16⁻¹ = 208 + 5 + 0.375 = 213.375
Comparing the decimal values: 770.5 (A) > 438.25 (C) > 213.375 (D) > 32.75 (B). Thus, the descending order is A, C, D, B.