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What is the decimal value of this 32-bit two's complement number? 1111 1111 1111 1111 1111 1111 1111 0110

What is the decimal value of this 32-bit two's complement number? 1111 1111 1111 1111 1111 1111 1111 0110

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Hello. Please answer the attached Computer Organization & Architecture question correctly. Please do not give a very lengthy explanation, just a sufficient one.

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### Converting a 32-bit Two's Complement Number to Decimal **Question: What is the decimal value of this 32-bit two's complement number?** ``` 1111 1111 1111 1111 1111 1111 1110 0110 ``` **Instructions:** *Show the details of your work. Please do not give an extremely long answer. Just a sufficient explanation.* --- **Solution:** 1. **Identify the Sign Bit:** - The most significant bit (leftmost bit) is `1`, which indicates that the number is negative since it uses two's complement representation. 2. **Find the Two's Complement:** - Flip all the bits of the number: ``` 0000 0000 0000 0000 0000 0000 0001 1001 ``` - Add `1` to the least significant bit (rightmost bit): ``` 0000 0000 0000 0000 0000 0000 0001 1001 + 1 --------------------------------- 0000 0000 0000 0000 0000 0000 0001 1010 ``` 3. **Convert Binary to Decimal:** - \( 0000 0000 0000 0000 0000 0000 0001 1010 \) - \( 1 \times 2^4 = 16 \) - \( 1 \times 2^3 = 8 \) - \( 0 \times 2^2 = 0 \) - \( 1 \times 2^1 = 2 \) - \( 0 \times 2^0 = 0 \) Adding these values together: \( 16 + 8 + 2 = 26 \) 4. **Apply the Negative Sign:** - Since the original number was negative, apply a negative sign to the decimal value. - Result: \( -26 \) --- Therefore, the decimal value of the given 32-bit two's complement number is **-26**.
Transcribed Image Text:### Converting a 32-bit Two's Complement Number to Decimal **Question: What is the decimal value of this 32-bit two's complement number?** ``` 1111 1111 1111 1111 1111 1111 1110 0110 ``` **Instructions:** *Show the details of your work. Please do not give an extremely long answer. Just a sufficient explanation.* --- **Solution:** 1. **Identify the Sign Bit:** - The most significant bit (leftmost bit) is `1`, which indicates that the number is negative since it uses two's complement representation. 2. **Find the Two's Complement:** - Flip all the bits of the number: ``` 0000 0000 0000 0000 0000 0000 0001 1001 ``` - Add `1` to the least significant bit (rightmost bit): ``` 0000 0000 0000 0000 0000 0000 0001 1001 + 1 --------------------------------- 0000 0000 0000 0000 0000 0000 0001 1010 ``` 3. **Convert Binary to Decimal:** - \( 0000 0000 0000 0000 0000 0000 0001 1010 \) - \( 1 \times 2^4 = 16 \) - \( 1 \times 2^3 = 8 \) - \( 0 \times 2^2 = 0 \) - \( 1 \times 2^1 = 2 \) - \( 0 \times 2^0 = 0 \) Adding these values together: \( 16 + 8 + 2 = 26 \) 4. **Apply the Negative Sign:** - Since the original number was negative, apply a negative sign to the decimal value. - Result: \( -26 \) --- Therefore, the decimal value of the given 32-bit two's complement number is **-26**.
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