**Title: Understanding Two’s Complement Representation in 8-bit Binary System**Assume numbers are represented in 8-bit two's complement representation. Show the calculation of the following:a. \(6 - 13\)b. \(-6 - 13\)---**Explanation:**In two's complement representation, positive numbers are represented as usual in binary, whereas negative numbers are represented by inverting the binary digits of the positive equivalent and adding one to the result. This representation allows for simple binary arithmetic and is commonly used in computer systems for signed number operations.To solve these computations, first convert the numbers to their 8-bit binary representations, perform the subtraction in binary by adding the two’s complement of the second number, and interpret the result.**Example Calculation:**1. **\(6 - 13\)**: - Convert \(6\) and \(13\) to binary. - Find the two’s complement of \(13\). - Add the binary of \(6\) to the two’s complement of \(13\).2. **\(-6 - 13\)**: - Convert \(-6\) and \(13\) to binary. - Find the two’s complement of both numbers. - Add the two’s complement of \(-6\) to the two’s complement of \(13\).These operations illustrate how subtractions are efficiently handled in binary using two’s complement, simplifying arithmetic operations within digital systems.

To perform subtraction using two's complement representation, you can follow these steps:Convert the…

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Engineering

Computer Science

Assume numbers are represented in 8-bit twos complement representation. Show the calculation of the following:

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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Question

**Title: Understanding Two’s Complement Representation in 8-bit Binary System**

Assume numbers are represented in 8-bit two's complement representation. Show the calculation of the following:

a. \(6 - 13\)

b. \(-6 - 13\)

---

**Explanation:**

In two's complement representation, positive numbers are represented as usual in binary, whereas negative numbers are represented by inverting the binary digits of the positive equivalent and adding one to the result. This representation allows for simple binary arithmetic and is commonly used in computer systems for signed number operations.

To solve these computations, first convert the numbers to their 8-bit binary representations, perform the subtraction in binary by adding the two’s complement of the second number, and interpret the result.

**Example Calculation:**

1. **\(6 - 13\)**:
- Convert \(6\) and \(13\) to binary.
- Find the two’s complement of \(13\).
- Add the binary of \(6\) to the two’s complement of \(13\).

2. **\(-6 - 13\)**:
- Convert \(-6\) and \(13\) to binary.
- Find the two’s complement of both numbers.
- Add the two’s complement of \(-6\) to the two’s complement of \(13\).

These operations illustrate how subtractions are efficiently handled in binary using two’s complement, simplifying arithmetic operations within digital systems.

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