Which of the following represents the two's complement of the binary number 1101?

To find the two's complement of the binary number 1101, we can follow these steps:

1. Break Down the Problem

To calculate the two's complement, we need to:

1. Invert the digits (change 0s to 1s and 1s to 0s).
2. Add 1 to the inverted binary number.

2. Relevant Concepts

The two's complement is computed as follows:

• Inversion of bits: If the binary number is represented as $b_n b_{n-1} ... b_1 b_0$, then the inversion yields $\overline{b_n} \overline{b_{n-1}} ... \overline{b_1} \overline{b_0}$.
• Adding 1 to the inverted number can be represented mathematically.

3. Analysis and Detail

Let's perform the operations step by step:

1. Original Binary Number: $1101$
2. Inversion:
   • Change each digit: $1 \to 0$ and $0 \to 1$.
   • Resulting inverted number: $0010$
3. Adding 1:
   • Binary addition of $0010$ and $0001$:

       0010
     + 0001
     ------
       0011
     

4. Verify and Summarize

We inversed the original number correctly and added 1 to the inverted binary number resulting in $0011$. Therefore, the two's complement of $1101$ is $0011$.

Final Answer

The two's complement of the binary number $1101$ is $0011$.