1. Perform the following subtraction using 10's complement on 532 - 794.
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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Transcribed Image Text:**Problem Statement:**
1. Perform the following subtraction using 10’s complement on 532 - 794.
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**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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