The given question belongs to the Electronics and Communication Engineering (ECE) category.

To represent a 4-bit code into a 7-bit even parity Hamming code, we need to follow certain steps. Let's go through each step in detail:

Step 1: Given 4-bit code: 1101

Step 2: Determine the number of parity bits required:
- The number of data bits in the given code is 4.
- The number of parity bits required can be found using the formula: 2^m >= (m + number of data bits + 1), where m is the number of parity bits.
- Substituting the values, we get: 2^m >= (m + 4 + 1)
- Solving this inequality, we find that m = 3 (since 2^3 = 8 >= 5)

Step 3: Insert the parity bits:
- In the 7-bit Hamming code, positions 1, 2, 4 are reserved for the parity bits, and positions 3, 5, 6, 7 are reserved for the data bits.
- Inserting the data bits in their respective positions, we get:
P1 1 P2 1 0 1 0

Step 4: Calculate the parity bits:
- The parity bits are calculated based on the positions of the 1's in the code.
- P1 is calculated based on the values in positions 3, 5, 7:
P1 = (1 + 0 + 0) % 2 = 1 (since there are two 0's and one 1)
- P2 is calculated based on the values in positions 3, 6, 7:
P2 = (1 + 0 + 0) % 2 = 1 (since there are two 0's and one 1)

Step 5: Insert the calculated parity bits in their respective positions:
- Inserting the calculated parity bits, we get:
1 1 1 1 0 1 0

Step 6: Verify even parity:
- The number of 1's in the entire 7-bit code (including the parity bits) should be even.
- Counting the number of 1's, we find that there are five 1's, which is an odd number.
- Since the parity is not even, we need to flip the value of the parity bit (P1) to make it even.
- Flipping the value of P1, we get:
0 1 1 1 0 1 0

Step 7: The final 7-bit even parity Hamming code representation of 1101 is:
0 1 1 1 0 1 0

Therefore, the correct answer is option 'A' (1010101).