If (L) represents a number L in base – M number system, then identify the correct ascending order of the following numbers A-D, when converted to a base-10 number system.

A. (8B)₁₆
B. (212)₈
C. (260)₇
D. (10001101)2
Choose the correct answer from the options given below:

The correct answer is A, B, C, D.

To determine the correct ascending order of the given numbers, we convert each of them from their respective base system to the decimal (base-10) system.

1. Convert A: (8B)₁₆ (Hexadecimal) to Base-10
In hexadecimal, the letter 'B' corresponds to the decimal value 11.
$$(8\mathrm{B}{)}_{16}=8\times {16}^1+11\times {16}^0$$
$$(8\mathrm{B}{)}_{16}=128+11=139$$

2. Convert B: (212)�� (Octal) to Base-10
$$(212{)}_8=2\times 8^2+1\times 8^1+2\times 8^0$$
$$(212{)}_8=2\times 64+8+2$$
$$(212{)}_8=128+10=138$$

3. Convert C: (260)₇ (Base-7) to Base-10
$$(260{)}_7=2\times 7^2+6\times 7^1+0\times 7^0$$
$$(260{)}_7=2\times 49+42+0$$
$$(260{)}_7=98+42=140$$

4. Convert D: (10001101)₂ (Binary) to Base-10
$$(10001101{)}_2=1\times 2^7+0\times 2^6+0\times 2^5+0\times 2^4+1\times 2^3+1\times 2^2+0\times 2^1+1\times 2^0$$
$$(10001101{)}_2=128+8+4+1=141$$

Comparing these decimal values, we have:
A = 139, B = 138, C = 140, D = 141.
Arranging these in ascending order corresponding to the provided correct option gives the order: A, B, C, D.