Explanation:

To understand why the correct answer is option 'C' (BCD), let's first briefly discuss what each of the given options represents:

- Gray Code: Gray code is a binary numeral system where two successive values differ in only one bit. It is commonly used in digital communication systems and is not directly related to representing decimal digits.

- Excess-3: Excess-3 code is a self-complementary binary-coded decimal (BCD) code. It represents decimal digits by adding 3 to the corresponding BCD digit. For example, the BCD digit 0 is represented as 0011 (binary) in Excess-3 code. However, this code is not used for directly representing the sum of two decimal digits.

- BCD: Binary-coded decimal (BCD) is a class of binary encodings of decimal numbers where each decimal digit is represented by a fixed number of bits. In BCD, each decimal digit is represented by a 4-bit binary code. For example, the decimal digit 2 is represented as 0010 (binary) in BCD. BCD is commonly used for representing decimal digits in digital systems.

Now, let's consider the given question: "The output sum of two decimal digits can be represented in ________."

When we add two decimal digits, the maximum sum we can get is 9+9=18, which can be represented using two decimal digits (e.g., 1 and 8). Since BCD is a binary code that represents decimal digits, it can be used to represent the sum of two decimal digits.

In BCD, each decimal digit is represented by a 4-bit code, which allows us to represent the sum of two decimal digits using a maximum of 8 bits (2 digits * 4 bits/digit). The sum can be represented as a combination of two BCD codes, one for each decimal digit.

For example, if we add the decimal digits 3 and 5, the sum is 8, which can be represented in BCD as 1000 (binary), where the first 4 bits represent the digit 0 and the second 4 bits represent the digit 8.

Therefore, the correct answer is option 'C' (BCD) because BCD is a binary code specifically designed for representing decimal digits, including the sum of two decimal digits.