If (L)M represents a number L in base-M number system, then identify the…

Concept — positional weights in any base

In a base-b positional system each digit is weighted by a power of the base fixed by its position. Reading outward from the radix point in either direction, the digits on its left carry the weights b0, b1, b2, … and the digits on its right carry b-1, b-2, …, so a numeral (dk…d1d0.f1f2)b equals the sum of every di·bi plus the sum of every fj / bj. Numerals written in different bases carry no common scale, so they can only be ranked after each one is re-expressed in a single shared base; decimal is the standard bridge for that.

Application — convert each numeral to decimal

1. (10110.11)2 = (1·16 + 0·8 + 1·4 + 1·2 + 0·1) + (1/2 + 1/4) = 22 + 0.75 = 22.75

2. (110.2)4 = (1·16 + 1·4 + 0·1) + (2/4) = 20 + 0.5 = 20.5

3. (32.5)8 = (3·8 + 2·1) + (5/8) = 26 + 0.625 = 26.625

4. (14.6)16 = (1·16 + 4·1) + (6/16) = 20 + 0.375 = 20.375

Cross-check — rank the decimal values

Ranking those decimal values from largest to smallest gives 26.625 > 22.75 > 20.5 > 20.375. The bottom two share the same integer part 20, so their fractional parts alone separate them: 2/4 = 0.5 exceeds 6/16 = 0.375. Reading the labels off that ranking, the descending order of the four numerals is (C), (A), (B), (D).