Introduction
Binary Coded Decimal (BCD) represents each decimal digit as a separate 4-bit binary pattern. Unlike pure binary, BCD keeps a one-to-one mapping between decimal digits and their encoded form — making it ideal for display drivers, calculators, and legacy financial hardware where human-readable decimal accuracy matters.
Our BCD converter encodes decimal integers into 8421 BCD and decodes BCD strings back to decimal, showing the nibble breakdown for every digit. Pair this with the Number System Converter when you need full base conversion beyond BCD.
8421 BCD Encoding Method
Each decimal digit 0–9 maps to its 4-bit binary equivalent (e.g. 5 → 0101). A multi-digit decimal number becomes a concatenation of these nibbles: 29 → 0010 1001. Invalid BCD uses patterns like 1010–1111 that do not represent any decimal digit.
Step-by-Step Examples
Example: Decimal 47 to BCD
4 → 0100, 7 → 0111. Combined BCD: 0100 0111 (often written 01000111 without spaces).
Example: BCD 1001 0000 to Decimal
Nibbles 1001 = 9 and 0000 = 0, giving decimal 90.
Real-Life Applications
- Seven-segment display and digital clock circuits
- Financial and accounting systems requiring exact decimal representation
- Microcontroller labs and digital electronics courses
- Understanding packed vs unpacked BCD in assembly language
- Historical mainframe and calculator architecture study
Advantages of Using This BCD Converter
- Clear nibble-by-nibble breakdown for each decimal digit
- Detects invalid BCD patterns automatically
- Educational output for lab reports and assignments
- Complements other number system tools on Numverto
- Free and works offline once the page is loaded
Common Mistakes to Avoid
- Treating BCD as ordinary binary (29 binary ≠ 29 BCD)
- Using 4-bit groups that are not valid BCD nibbles
- Dropping leading zeros in individual digit encodings
- Confusing packed BCD (two digits per byte) with unpacked layouts
- Forgetting that BCD is less storage-efficient than pure binary