Assuming an integer is saved in 8 bits and negative integers in 2's complement, what is the result of  12210 + 10110

To solve \( 122_{10} + 101_{10} \) using an 8-bit system and 2's complement for negative numbers, follow these steps:

1. **Convert both numbers to binary**:
   - \( 122_{10} \) to binary: \( 01111010_2 \) (8 bits)
   - \( 101_{10} \) to binary: \( 01100101_2 \) (8 bits)

2. **Add the two binary numbers**:
   - \( 01111010_2 + 01100101_2 \)
   - Perform binary addition:

\[
\begin{aligned}
01111010_2 \\
+ 01100101_2 \\
\hline
11011111_2
\end{aligned}
\]

3. **Check the result**:
   - The result is \( 11011111_2 \), which is the binary representation in 8 bits.

4. **Interpret the result**:
   - Since the most significant bit (MSB) is 1, it indicates that the result is negative (because of the 2's complement representation).
   - To find the decimal value of this negative number, first find the 2's complement (invert the bits and add 1):
     - Invert the bits: \( 00100000_2 \)
     - Add 1: \( 00100001_2 \)

     This equals \( 33_{10} \).

   - So, \( 11011111_2 \) represents \( -33_{10} \) in 2's complement form.

Thus, the result of \( 122_{10} + 101_{10} \) in an 8-bit system using 2's complement is \( -33_{10} \).

---

Would you like more details on any specific step, or have any questions?

Here are 5 related questions you might find interesting:
1. How does 2's complement work for larger bit systems, like 16-bit or 32-bit?
2. What happens in binary addition when the result exceeds the bit limit (overflow)?
3. Can you demonstrate how to subtract two numbers in 2's complement?
4. How do signed and unsigned integers differ in binary systems?
5. What are some common errors when converting negative decimal numbers to binary?

**Tip**: In binary arithmetic, always watch for overflow when the sum exceeds the bit limit.

Assuming an integer is saved in 8 bits and negative integers in 2's complement, what is the result of 12210 + 10110?

Discover how to perform binary addition with 8-bit integers, including handling negative numbers using 2's complement. The detailed solution covers converting decimal numbers to binary, performing binary addition, and interpreting the result in 2's complement format. Suitable for students in Grades 9-12.

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