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 ascending order of the following numbers A-D when converted to decimal number system.
A. (11011.11)2
B. (131.2)4
C. (25.5)8
D. (16.6)16
Choose the correct answer from the options given below:
Answer: B. C, D, A, B — ConceptIn a positional number system of base b, each digit is multiplied by a power of b determined by its position relative to the radix point. Digits to the…
- A.
C, D, B, A
- B.
C, D, A, B
- C.
A, C, D, B
- D.
B, A, C, D
Attempted by 10 students.
Show answer & explanation
Correct answer: B
Concept
In a positional number system of base b, each digit is multiplied by a power of b determined by its position relative to the radix point.
Digits to the left use powers b0, b1, b2, … from right to left, while fractional digits to the right use b-1, b-2, … . The decimal value is the sum of these place values.
Application
Convert each given numeral independently and then compare the four decimal values:
A = (11011.11)2 = 1×24 + 1×23 + 0×22 + 1×21 + 1×20 + 1×2-1 + 1×2-2 = 16 + 8 + 0 + 2 + 1 + 0.5 + 0.25 = 27.75.
B = (131.2)4 = 1×42 + 3×41 + 1×40 + 2×4-1 = 16 + 12 + 1 + 0.5 = 29.5.
C = (25.5)8 = 2×81 + 5×80 + 5×8-1 = 16 + 5 + 0.625 = 21.625.
D = (16.6)16 = 1×161 + 6×160 + 6×16-1 = 16 + 6 + 0.375 = 22.375.
Cross-check
The values form two clear pairs: C = 21.625 is below D = 22.375, and A = 27.75 is below B = 29.5; also D < A. Therefore the complete ascending chain is C < D < A < B.
Thus the required ascending order is C, D, A, B.