### Arithmetic System with 3-Digit Decimal Numbers in BCD NotationThe following information and problems pertain to an arithmetic system that operates with 3-digit decimal numbers using Binary-Coded Decimal (BCD) notation. The system employs a 12-bit representation: negative numbers utilize the 10's complement form, and one decimal digit (4 bits) is occupied by the sign (0 for "+", 9 for "-").#### 1. Problems and Exercises1. **Determine the Range of the System:** 1a) Identify the most positive and the most negative numbers in both decimal and BCD forms.2. **Number Representation in BCD:** 1b) Represent the numbers $ A = +36 $ and $ B = -42 $ in BCD notation. 3. **Calculate Complements:** 1c) Calculate the 10's complements of $ A $ and $ B $ in BCD.4. **Perform BCD Arithmetic Operations:** 1d) Conduct the following operations in BCD bit-by-bit, making sure to show carries and apply the BCD correction (add 6) when necessary (i.e., when the sum of two decimal digits is greater than 9): - 1d1) $ A + B $ in BCD. - 1d2) $ A - B $ in BCD by adding $ A $ and the 10's complement of $ B $. - 1d3) $ B - A $ in BCD by adding $ B $ and the 10's complement of $ A $.These exercises will help in understanding the application of BCD in arithmetic operations, handling negative numbers using the 10's complement method, and ensuring accuracy in BCD arithmetic through carry handling and necessary corrections.

BCD form:In BCD form, each decimal digit is represented by a 4-bit binary code. They provide direct…

1. An arithmetic system operates with 3-digit decimal numbers with sign presented in BCD (12 bits), negative numbers utilize the 10's complement form, one decimal digit (4 bits) is occupied by sign: 0 for "+" and 9 for "-". 1a) Show the most positive and the most negative numbers in both decimal and BCD forms. 1b) Present numbers A=+36 and B= -42 in BCD. 1c) Present the 10's complements of A and B in BCD.

1. An arithmetic system operates with 3-digit decimal numbers with sign presented in BCD (12 bits), negative numbers utilize the 10's complement form, one decimal digit (4 bits) is occupied by sign: 0 for "+" and 9 for "-". 1a) Show the most positive and the most negative numbers in both decimal and BCD forms. 1b) Present numbers A=+36 and B= -42 in BCD. 1c) Present the 10's complements of A and B in BCD.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Code Conversion

The method or technique used to convert code from one format to another is termed code conversion. Code conversions are most commonly used in computers, digital electronics, microprocessors, etc.

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### Arithmetic System with 3-Digit Decimal Numbers in BCD Notation

The following information and problems pertain to an arithmetic system that operates with 3-digit decimal numbers using Binary-Coded Decimal (BCD) notation. The system employs a 12-bit representation: negative numbers utilize the 10's complement form, and one decimal digit (4 bits) is occupied by the sign (0 for "+", 9 for "-").

#### 1. Problems and Exercises

1. **Determine the Range of the System:**

1a) Identify the most positive and the most negative numbers in both decimal and BCD forms.

2. **Number Representation in BCD:**

1b) Represent the numbers $ A = +36 $ and $ B = -42 $ in BCD notation.

3. **Calculate Complements:**

1c) Calculate the 10's complements of $ A $ and $ B $ in BCD.

4. **Perform BCD Arithmetic Operations:**

1d) Conduct the following operations in BCD bit-by-bit, making sure to show carries and apply the BCD correction (add 6) when necessary (i.e., when the sum of two decimal digits is greater than 9):

- 1d1) $ A + B $ in BCD.
- 1d2) $ A - B $ in BCD by adding $ A $ and the 10's complement of $ B $.
- 1d3) $ B - A $ in BCD by adding $ B $ and the 10's complement of $ A $.

These exercises will help in understanding the application of BCD in arithmetic operations, handling negative numbers using the 10's complement method, and ensuring accuracy in BCD arithmetic through carry handling and necessary corrections.

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