 # Binary-Coded Decimal

## Definition of Binary-Coded Decimal

Binary-Coded Decimal (BCD) is a class of binary encodings where each decimal digit is represented by a fixed number of binary digits, usually four or eight. In BCD, a decimal number is split into individual digits and each digit is then represented by its binary equivalent. It is a simple way of converting decimal numbers to a more computer-friendly format, however, it can be less efficient than pure binary when it comes to arithmetic operations and storage.

### Phonetic

Binary-Coded Decimal: /ˈbʌɪnəri ˈkoʊdəd dɪˈsɪməl/

## Key Takeaways

1. Binary-Coded Decimal (BCD) is a class of binary encodings where each decimal digit is represented by a fixed number of binary digits, usually 4 or 8 bits.
2. BCD is more human-readable and easily convertible to and from decimal representation, which is why it is widely used in calculators, electronic meters, and financial systems.
3. Although BCD simplifies data interpretation, it is less efficient in terms of storage and processing compared to pure binary representation.

## Importance of Binary-Coded Decimal

Binary-Coded Decimal (BCD) is an important technology term as it represents a class of binary encodings of decimal numbers where each decimal digit is represented by a fixed number of binary digits, usually four or eight.

BCD’s significance lies in its ability to bridge the gap between the binary numeral system, which computers use to perform calculations, and the decimal system that humans commonly work with.

By employing BCD, computers can efficiently process, store, and display decimal numbers without incurring the potential issues associated with floating-point approximations.

This results in enhanced accuracy in various applications such as financial calculations, banking transactions, and real-time systems where precise results are paramount.

## Explanation

Binary-Coded Decimal (BCD) serves a significant purpose in the context of digital systems and data representation, particularly when dealing with numerical data related to human interaction. Its primary use is to accurately represent decimal numbers in binary form, simplifying the process of handling and exchanging data between digital and analog systems.

This representation allows for more straightforward conversions and display of decimal numbers, ensuring that calculations and data remained consistent and easily understandable for users operating digital systems, such as computers, calculators, and financial applications. BCD is particularly useful in situations where decimal precision is crucial, such as financial calculations, where even a small rounding error can have significant consequences.

The BCD system encodes each decimal digit (0-9) as a 4-bit binary number, making it easier for humans to interpret and work with the values, as compared to traditional binary number representation. Additionally, BCD encoding mitigates potential errors that might occur during the conversion between binary and decimal representations.

This user-friendly data representation plays a crucial role in avoiding misinterpretation and ensuring accurate calculations, significantly impacting industries where error-free digital data handling is of paramount importance.

## Examples of Binary-Coded Decimal

Binary-Coded Decimal (BCD) is a class of binary encodings, where each decimal digit is represented by a fixed number of binary digits (usually four). Here are three real-world examples of BCD technology:

Calculators: BCD is commonly used in electronic calculators for performing arithmetic operations with decimal numbers. It provides accurate calculations by avoiding floating-point errors, which can lead to inaccurate results. Internally, calculators store and manipulate numbers using BCD to ensure reliable and precise calculations.

Digital displays: BCD is often used in digital displays, such as on digital clocks, meters, and other electronic devices that show decimal numbers. The BCD representation allows for easy conversion from the stored binary value to the actual decimal digits that need to be displayed on the screen. One common method for implementing this is the use of a 7-segment display, which represents each decimal digit as a combination of seven illuminated segments.

Legacy computing systems: BCD technology was widely used in early computing systems, such as mainframes and punch card systems, to perform arithmetic operations efficiently. Older processors like IBM System/360 and Intel x86 (through BCD instructions) supported BCD for arithmetic operations in their instruction set architecture. Although modern computing systems primarily use binary representations for numbers, some software and hardware still rely on BCD for compatibility and specific tasks that require accurate decimal representation.

## FAQ: Binary-Coded Decimal

### 1. What is Binary-Coded Decimal?

Binary-Coded Decimal (BCD) is a class of binary encodings where each decimal digit is represented by a fixed number of bits, typically 4 or 8. It is a way to express decimal numbers in a binary form that simplifies certain arithmetic operations and allows easier storage and manipulation of decimal digits.

### 2. Why is Binary-Coded Decimal used?

BCD is used because it allows for easier conversion between binary and decimal representations. It also simplifies the storage and manipulation of decimal numbers, making it useful in certain applications where decimal arithmetic is required, such as financial computations, electronic devices, and calculators.

### 3. How is Binary-Coded Decimal different from Binary numbers?

The main difference between BCD and binary numbers is their representation of decimal digits. In BCD, each decimal digit is stored in its own group of binary bits, whereas in binary representation, the entire number is represented as a single continuous sequence of bits. This makes BCD more straightforward when dealing with decimal numbers but less efficient in terms of storage space compared to binary representation.

### 4. How do I convert a decimal number to Binary-Coded Decimal?

To convert a decimal number to BCD, follow these steps:
1. Break the decimal number into its individual digits.
2. Convert each decimal digit to its 4-bit binary equivalent.
3. Combine the binary digits of each decimal digit to form the BCD representation of the number.

### 5. How do I convert a Binary-Coded Decimal number to decimal?

To convert a BCD number to decimal, follow these steps:
1. Separate the BCD number into its individual 4-bit groups, each representing a decimal digit.
2. Convert each 4-bit binary group to its decimal equivalent.
3. Combine the decimal digits to form the decimal representation of the number.

## Related Technology Terms

• Bit combination
• Packed BCD
• Decimal digit