## Introduction

Binary Coded Decimal or BCD is a system of representing decimal numbers using binary notation. In BCD, each decimal digit is represented by a four-bit binary code. BCD was commonly used in early digital computers and is still used in some specialized applications, such as in electronic calculators and digital clocks.

## Characteristics

BCD is a self-contained system that can be used to perform arithmetic operations on decimal numbers using binary logic circuits. Each decimal digit is represented by a unique combination of four bits, allowing easy conversion between binary and decimal representations.

## Construction

BCD is constructed by dividing each decimal digit into two parts, with the most significant digit represented by the four high-order bits and the least significant digit represented by the four low-order bits. Each digit is then represented by a unique four-bit code, as shown in the table below.

## Working

BCD works by using binary addition to perform arithmetic operations on decimal numbers. To add two BCD numbers, the four bits representing each decimal digit are added together using binary addition. If the result of the addition is greater than 9 (the maximum value for a single decimal digit), the carry from that digit is added to the next higher-order digit.

## Procedure

To convert a decimal number to BCD, each decimal digit is represented by its four-bit BCD code. To convert a BCD number to decimal, each group of four bits is converted to its decimal equivalent, and the resulting decimal digits are combined to form the final decimal number.

## Rules

BCD has the advantage of being easy to understand and implement, but it has some limitations. One limitation is that BCD requires more bits to represent a given number than traditional binary notation, which can be inefficient in terms of memory usage.

## Formula

There is no specific formula for BCD, as it is simply a way of representing decimal numbers using binary notation.

## Need

The need for Binary Coded Decimal (BCD) arises from the requirement to represent decimal numbers in digital systems. In many applications, decimal numbers are commonly used, such as in finance, accounting, and timekeeping, and therefore, it is necessary to represent decimal numbers in digital form.

The following are some specific needs for BCD:

- Decimal representation: BCD allows for the direct representation of decimal numbers in digital form, which is important in applications where decimal numbers are commonly used.
- Accuracy: BCD provides an accurate representation of decimal numbers, which is critical in applications such as accounting and finance.
- Ease of use: BCD is easy to understand and work with since it is based on the familiar decimal numbering system.
- Compatibility: BCD is compatible with many digital systems, making it a widely used format for representing decimal numbers.
- Efficient processing: BCD can be processed using simple arithmetic operations, making it easy to integrate into digital systems and efficient to process.
- Human-readable output: BCD can be easily converted back into decimal form, making it easy to display the output of digital systems to humans.

## Applications

- Electronic calculators
- Digital clocks and watches
- Point of sale (POS) systems
- Industrial control systems
- Medical equipment
- Aviation and aerospace systems
- Banking and financial systems.