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thể trace of the signed-magnitude plication algori gnitude are four bits.

thể trace of the signed-magnitude plication algori gnitude are four bits.

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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**Understanding the Signed-Magnitude Multiplication Algorithm** This section covers the signed-magnitude multiplication algorithm with a focus on multiplying two negative numbers, specifically (-9) * (-11). In this example, all magnitudes are represented using four bits. **Steps:** 1. **Representation:** - Convert the numbers to binary, ensuring each is represented with four bits. - For signed-magnitude representation, the leftmost bit is the sign bit: 0 for positive and 1 for negative. 2. **Multiplication:** - Multiply the absolute binary values of the numbers. - Consider the signs of the numbers to determine the final sign of the product. 3. **Result:** - Convert the product back to signed-magnitude form, maintaining the correct number of bits. By following these steps, you can trace how the algorithm processes the numbers to yield the final product. A detailed step-by-step calculation is provided below: - **Step 1:** Convert -9 and -11 to signed-magnitude binary form. - **Step 2:** Multiply their absolute values, neglecting the sign initially. - **Step 3:** Determine the sign of the result based on the original signs (− × − = +). - **Step 4:** Convert the result to four-bit signed-magnitude form and verify correctness. Understanding this algorithm is fundamental in computer science and digital electronics, especially in designing systems that efficiently handle arithmetic operations involving signed numbers.
Transcribed Image Text:**Understanding the Signed-Magnitude Multiplication Algorithm** This section covers the signed-magnitude multiplication algorithm with a focus on multiplying two negative numbers, specifically (-9) * (-11). In this example, all magnitudes are represented using four bits. **Steps:** 1. **Representation:** - Convert the numbers to binary, ensuring each is represented with four bits. - For signed-magnitude representation, the leftmost bit is the sign bit: 0 for positive and 1 for negative. 2. **Multiplication:** - Multiply the absolute binary values of the numbers. - Consider the signs of the numbers to determine the final sign of the product. 3. **Result:** - Convert the product back to signed-magnitude form, maintaining the correct number of bits. By following these steps, you can trace how the algorithm processes the numbers to yield the final product. A detailed step-by-step calculation is provided below: - **Step 1:** Convert -9 and -11 to signed-magnitude binary form. - **Step 2:** Multiply their absolute values, neglecting the sign initially. - **Step 3:** Determine the sign of the result based on the original signs (− × − = +). - **Step 4:** Convert the result to four-bit signed-magnitude form and verify correctness. Understanding this algorithm is fundamental in computer science and digital electronics, especially in designing systems that efficiently handle arithmetic operations involving signed numbers.
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