Gray Code Conversion:

Gray code, also known as reflected binary code, is a binary numeral system where adjacent values only differ by one bit. It is commonly used in various applications such as communication systems, rotary encoders, and error detection.

To convert a decimal number to Gray code, we can follow a simple algorithm:

1. Write down the binary representation of the given decimal number.
2. Start from the leftmost bit (MSB) and copy it as the leftmost bit of the Gray code.
3. For each subsequent bit, copy the XOR (exclusive OR) of the current bit with the previous bit of the binary representation.
4. Repeat this process until all bits have been converted.

Conversion of 14 to Gray Code:

To convert the number 14 to Gray code, we first need to write down its binary representation.

14 in binary is 1110.

Now, let's convert this binary number to Gray code using the algorithm mentioned above:

- Start with the leftmost bit: 1 (MSB).
- Copy the MSB as the leftmost bit of the Gray code: 1.
- Move to the next bit: 1.
- Take the XOR of the current bit (1) with the previous bit (1): 1 XOR 1 = 0.
- Copy the result (0) as the next bit of the Gray code: 10.
- Move to the next bit: 1.
- Take the XOR of the current bit (1) with the previous bit (0): 1 XOR 0 = 1.
- Copy the result (1) as the next bit of the Gray code: 101.
- Move to the next bit: 0.
- Take the XOR of the current bit (0) with the previous bit (1): 0 XOR 1 = 1.
- Copy the result (1) as the next bit of the Gray code: 1011.

Therefore, the Gray code equivalent of the number 14 is 1011.

Answer:
The correct answer is option D, which is 1001.