The image contains a request to perform binary addition of $-15$ and $6$. To do this, let's first convert the decimal numbers to their binary form and then perform the addition.

Steps:

1. Convert the decimal numbers $-15$ and $6$ to binary:

   • Binary of $6$ is straightforward: $6_{10} = 110_2$.
   • Binary of $-15$ will be represented using the two's complement method in binary. We need to first convert $15$ to binary, then take its two's complement.

2. Perform the addition in binary.

Let me work through this now.Here's the binary representation of the numbers:

• $-15$ in 8-bit two's complement is: 11110001.
• $6$ in binary is: 00000110.

After performing binary addition, the result is $-9$, which in 8-bit two's complement is: 11110111.

Summary:

• $-15$ in binary: 11110001
• $6$ in binary: 00000110
• $-9$ in binary: 11110111

Would you like more details on how binary addition works, or any further clarifications?

Here are some related questions to explore:

1. How does two's complement represent negative numbers?
2. What happens during binary addition when there's an overflow?
3. How does two's complement affect subtraction?
4. How can binary operations be used in computer arithmetic?
5. What are the applications of two's complement in programming?

Tip: Two's complement is commonly used because it simplifies the hardware design for performing addition and subtraction in binary systems.