To understand why the correct answer is option 'D' (0, 1, 2, 3), let's break down the problem and analyze it step by step.

1. Binary Numbers:
Binary numbers are numbers that are expressed in base 2, using only two digits: 0 and 1. Each digit in a binary number represents a power of 2. For example, the binary number 1010 represents (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (0 * 2^0) = 10 in decimal.

2. Decimal Equivalents:
The decimal equivalent of a binary number is the number obtained by converting the binary representation to base 10. For example, the decimal equivalent of the binary number 1010 is 10.

3. Divisibility by 4:
A number is divisible by 4 if its last two digits (in binary representation) form a number that is divisible by 4. In other words, the remainder when dividing a binary number by 4 is determined by the last two digits of the binary number.

4. DFA (Deterministic Finite Automaton):
A DFA is a finite state machine that accepts or rejects strings of symbols, according to a set of predetermined rules. In this case, the DFA accepts binary numbers whose decimal equivalent is divisible by 4.

Now, let's consider all the possible remainders when dividing binary numbers (whose decimal equivalent is divisible by 4) by 4:

a) Remainder 0:
A binary number is divisible by 4 if its last two digits are 00. Therefore, the remainders 0, 4, 8, 12, 16, etc., are all possible when dividing binary numbers by 4.

b) Remainder 1:
A binary number is not divisible by 4 if its last two digits are 01. Therefore, the remainder 1, 5, 9, 13, 17, etc., are not possible when dividing binary numbers by 4.

c) Remainder 2:
A binary number is divisible by 4 if its last two digits are 10. Therefore, the remainders 2, 6, 10, 14, 18, etc., are all possible when dividing binary numbers by 4.

d) Remainder 3:
A binary number is not divisible by 4 if its last two digits are 11. Therefore, the remainder 3, 7, 11, 15, 19, etc., are not possible when dividing binary numbers by 4.

In summary, the possible remainders when dividing binary numbers (whose decimal equivalent is divisible by 4) are 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, etc. However, since we are considering only the remainders less than 4, the correct answer is option 'D' (0, 1, 2, 3).