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1. Perform the following subtraction using 10's complement on 532 - 794.

1. Perform the following subtraction using 10's complement on 532 - 794.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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**Problem Statement:** 1. Perform the following subtraction using 10’s complement on 532 - 794. --- **Explanation:** To solve this subtraction using the 10's complement method, follow these steps: 1. **Determine the 10's Complement of the Subtrahend (794):** - Add leading zeros to make both numbers the same length, if necessary. In this case, both numbers are already 3 digits. - Subtract each digit from 9: - For 794: - 9 - 7 = 2 - 9 - 9 = 0 - 9 - 4 = 5 - Add 1 to the result: - 205 + 1 = 206 2. **Add the 10's Complement of the Subtrahend to the Minuend (532):** - 532 + 206 = 738 3. **Check for a Carry:** - Since we're working with 3-digit numbers, look at the fourth digit (if a carry occurs, it should be a 1 in the thousands place). - In this case, there is no carry, meaning the result is already negative. 4. **Convert Back (if necessary):** - If there is no carry, take the 10's complement of the result (738) and place a negative sign. - 10's complement of 738: - 9 - 7 = 2 - 9 - 3 = 6 - 9 - 8 = 1 - Add 1: - 261 + 1 = 262 - Hence, the result of 532 - 794 is -262. This illustrates how subtraction can efficiently be performed using the 10's complement method, especially when dealing with larger numbers or binary representations.
Transcribed Image Text:**Problem Statement:** 1. Perform the following subtraction using 10’s complement on 532 - 794. --- **Explanation:** To solve this subtraction using the 10's complement method, follow these steps: 1. **Determine the 10's Complement of the Subtrahend (794):** - Add leading zeros to make both numbers the same length, if necessary. In this case, both numbers are already 3 digits. - Subtract each digit from 9: - For 794: - 9 - 7 = 2 - 9 - 9 = 0 - 9 - 4 = 5 - Add 1 to the result: - 205 + 1 = 206 2. **Add the 10's Complement of the Subtrahend to the Minuend (532):** - 532 + 206 = 738 3. **Check for a Carry:** - Since we're working with 3-digit numbers, look at the fourth digit (if a carry occurs, it should be a 1 in the thousands place). - In this case, there is no carry, meaning the result is already negative. 4. **Convert Back (if necessary):** - If there is no carry, take the 10's complement of the result (738) and place a negative sign. - 10's complement of 738: - 9 - 7 = 2 - 9 - 3 = 6 - 9 - 8 = 1 - Add 1: - 261 + 1 = 262 - Hence, the result of 532 - 794 is -262. This illustrates how subtraction can efficiently be performed using the 10's complement method, especially when dealing with larger numbers or binary representations.
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