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. (11111.11)₂
B. (102.3)₆
C. (42.5)₈
D. (32.6)₁₆
Choose the correct answer from the options given below:

Stepwise Solution: Convert Each Number to Decimal
We are given four numbers in different bases. We need to convert each to decimal and then arrange them in ascending order.
A. $$\bf{(11111.11)_2}$$​ → Base 2 to Decimal
​$$11111.11_2 = (1 \times 2^4) + (1 \times 2^3) + (1 \times 2^2) + (1 \times 2^1) + (1 \times 2^0) + (1 \times 2^{-1}) + (1 \times 2^{-2})$$​​
​$$= (1×16) + (1×8) + (1×4) + (1×2) + (1×1) + (1×\frac{1}{2}) + (1×\frac{1}{4})$$​​
​$$= 16 + 8 + 4 + 2 + 1 + 0.5 + 0.25 = 31.75$$​​
B. $$\bf{(102.3)_6}$$​ → Base 6 to Decimal
​$$102.3_6 = (1 \times 6^2) + (0 \times 6^1) + (2 \times 6^0) + (3 \times 6^{-1})$$​​
​$$= (1×36) + (0×6) + (2×1) + (3×\frac{1}{6})$$​​
​$$= 36 + 0 + 2 + 0.5 = 38.5$$​​
C. $$\bf{(42.5)_8}$$​ → Base 8 to Decimal
​$$42.5_8 = (4 \times 8^1) + (2 \times 8^0) + (5 \times 8^{-1})$$​​
​$$= (4×8) + (2×1) + (5×\frac{1}{8})$$​​
​$$= 32 + 2 + 0.625 = 34.625$$​​
D. $$\bf{(32.6)_{16}}$$​ → Base 16 to Decimal
Convert hexadecimal digits:
3 → 3, 2 → 2, 6 → 6
​$$32.6_{16} = (3 \times 16^1) + (2 \times 16^0) + (6 \times 16^{-1})$$​​
​$$= (3×16) + (2×1) + (6×\frac{1}{16})$$​​
​$$= 48 + 2 + 0.375 = 50.375$$​​

Ascending Order of Values:
31.75 (A) < 34.625 (C) < 38.5 (B) < 50.375 (D)
Arranging them in ascending order results in the sequence: A < C < B < D.
Information Booster:
1. Binary to Decimal (Base 2): Multiply each bit with $$2^n$$​, where n decreases from left to right.
2. Octal to Decimal (Base 8): Multiply each digit with $$8^n$$​, same logic as base-10 but with 8 as base.
3. Hexadecimal to Decimal (Base 16): Uses digits 0–9 and letters A–F (A=10, B=11,…F=15).
4. Positional Notation: Any number in base b is converted to decimal using the formula:
​$$\sum_{i=0}^{n} d_i \cdot b^i + \sum_{j=1}^{m} d_{-j} \cdot b^{-j}$$​​​​​​