BCD (Binary-Coded Decimal) Converter
Convert between decimal numbers and Binary-Coded Decimal (BCD) format. Master BCD encoding used in digital displays, calculators, and embedded systems with detailed explanations and examples.
BCD (Binary-Coded Decimal) Converter
Convert between decimal numbers and Binary-Coded Decimal (BCD) format.
BCD Format
Each decimal digit is represented by exactly 4 binary bits.
Understanding Binary-Coded Decimal (BCD)
What is BCD?
Binary-Coded Decimal (BCD) is a binary encoding method where each decimal digit (0-9) is represented by exactly four binary bits (a nibble). Unlike pure binary representation, BCD maintains a direct correspondence between decimal digits and their binary representation.
In BCD, the number 1234 becomes 0001 0010 0011 0100, where each group of four bits represents one decimal digit. This encoding method bridges the gap between human-readable decimal numbers and computer-readable binary data.
BCD is particularly useful in applications where decimal precision is critical and where frequent conversion between binary and decimal is required, such as in digital displays, calculators, and financial systems.
BCD vs Pure Binary
Example: Number 25
BCD Advantages
Easier decimal conversion, no rounding errors, direct digit manipulation
BCD Disadvantages
Less storage efficient, more complex arithmetic operations
BCD Encoding Reference
Standard BCD Encoding
| Decimal | BCD (4-bit) |
|---|---|
| 0 | 0000 |
| 1 | 0001 |
| 2 | 0010 |
| 3 | 0011 |
| 4 | 0100 |
| 5 | 0101 |
| 6 | 0110 |
| 7 | 0111 |
| 8 | 1000 |
| 9 | 1001 |
BCD Examples
Types of BCD Encoding
Unpacked BCD
In unpacked BCD, each decimal digit occupies a full byte (8 bits), with the upper 4 bits typically set to zero and the lower 4 bits containing the BCD value.
Example: 25
Packed BCD
In packed BCD, two decimal digits are stored in a single byte, with each digit occupying 4 bits. This is more storage efficient than unpacked BCD.
Example: 25
Real-World Applications of BCD
Digital Displays
Seven-segment displays and LCD panels often use BCD encoding for direct digit-to-display conversion. Each BCD nibble can directly drive display decoder circuits without complex conversion.
Financial Systems
Banks and financial institutions use BCD to avoid rounding errors in decimal calculations. BCD ensures exact representation of currency values and maintains precision in accounting applications.
Embedded Systems
Microcontrollers in calculators, digital clocks, and measurement instruments use BCD for easy interfacing with numeric displays and human-readable output formatting.
Data Storage
Database systems use packed BCD for storing decimal numbers with fixed precision, especially in financial and scientific applications where exact decimal representation is crucial.
Legacy Systems
Mainframe computers and legacy business systems extensively use BCD for data processing and storage, particularly in COBOL applications and older financial systems.
Industrial Control
PLCs (Programmable Logic Controllers) and industrial automation systems use BCD for interfacing with operator panels, displays, and data acquisition systems in manufacturing environments.
Step-by-Step Tutorial: Converting 1234 to BCD
Converting Decimal 1234 to BCD
Step 1: Separate Digits
Break down 1234 into individual digits
Step 2: Convert Each Digit
Step 3: Combine Results
Concatenate all 4-bit groups
Step 4: Verification
Check the conversion
Final Result:
1234₁₀ = 0001 0010 0011 0100₍BCD₎
Related Number Tools
Frequently Asked Questions
What is the difference between BCD and binary?
BCD encodes each decimal digit separately using 4 bits, while binary represents the entire number as a single binary value. For example, 25 in binary is 11001 (5 bits), but in BCD it is 0010 0101 (8 bits). BCD maintains decimal digit boundaries, making conversion easier but less storage efficient.
Why use BCD instead of pure binary?
BCD is used when decimal precision is critical and frequent decimal-binary conversion is needed. It prevents rounding errors in financial calculations, simplifies display interfacing, and makes debugging easier since each nibble directly corresponds to a decimal digit. However, it uses more storage and makes arithmetic operations more complex.
What happens to invalid BCD codes?
BCD only uses 10 out of 16 possible 4-bit combinations (0000-1001). The codes 1010-1111 (A-F in hex) are invalid in BCD. When encountered, these typically trigger error conditions in BCD arithmetic circuits or are treated as special cases depending on the implementation.
How is BCD arithmetic performed?
BCD arithmetic requires special adjustment after binary operations. For addition, if a nibble sum exceeds 9 or generates a carry, 6 is added to adjust the result. For subtraction, if borrowing occurs, 10 is borrowed instead of 16. Multiplication and division are more complex and often use repeated addition/subtraction algorithms.
Where is packed BCD commonly used?
Packed BCD is widely used in database systems (like IBM DB2), mainframe computers, COBOL programs, and embedded systems where storage efficiency matters but decimal precision is required. Financial institutions use it for currency calculations, and industrial systems use it for precise measurement storage.