Find the additive inverse (negate) the value given in 8-bit two's complement representation as 00000110.



To find the additive inverse (negation) of a number given in 8-bit two's complement representation, you follow these steps:

1. **Start with the original binary number:**  
   The given number is \( 00000110 \).

2. **Invert all the bits:**  
   Flipping each bit of \( 00000110 \) gives us \( 11111001 \).

3. **Add 1 to the inverted number:**  
   Adding 1 to \( 11111001 \):

   \[
   11111001 + 1 = 11111010
   \]

Therefore, the additive inverse of \( 00000110 \) in 8-bit two's complement representation is \( 11111010 \).

### Explanation:

- The original number \( 00000110 \) is equivalent to the decimal number \( 6 \).
- The result \( 11111010 \) represents \( -6 \) in two's complement form.

Would you like further details or have any questions? Here are some related questions for further exploration:

1. How do you find the additive inverse of a negative number in 8-bit two's complement?
2. What is the range of values that can be represented using 8-bit two's complement?
3. How does two's complement representation differ from one's complement?
4. What is the two's complement representation of the decimal number \(-128\)?
5. How can you verify that \( 11111010 \) represents \(-6\) in decimal?

**Tip:** Remember, two's complement representation allows for easy negation and representation of both positive and negative integers.

Learn how to find the additive inverse (negate) of the binary number 00000110 in 8-bit two's complement representation. Step-by-step guide with detailed explanations and examples. Suitable for students and enthusiasts of binary arithmetic and computer science.

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