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
Learn More
What is Binary Coded Decimal (BCD)?
Binary Coded Decimal (BCD) is a class of binary encodings where each decimal digit is represented by its own fixed-length binary sequence. In standard 8421 BCD, each decimal digit (0–9) is encoded using exactly 4 bits. This encoding is fundamental in digital electronics courses and frequently appears in BCA, BTech, and diploma examinations.
How BCD Encoding Works
Unlike pure binary conversion where the entire number is converted at once, BCD processes each decimal digit independently:
- Decimal 0 → 0000
- Decimal 5 → 0101
- Decimal 9 → 1001
For the decimal number 42, we encode digit 4 as 0100 and digit 2 as 0010, giving BCD: 0100 0010.
BCD vs Regular Binary
Decimal 42 in regular binary is 101010 (base 2), but in BCD it is 0100 0010. BCD uses more bits but preserves exact decimal representation, which is critical in financial calculations where rounding errors from floating-point binary are unacceptable.
Types of BCD
8421 BCD (Standard)
The most common form where each 4-bit group weights are 8, 4, 2, 1. Invalid combinations (1010–1111) are not used for digits.
Excess-3 BCD
Each digit is encoded by adding 3 before converting to binary. Used in some arithmetic circuits.
Applications of BCD
- Seven-segment display drivers
- Electronic calculators
- Banking and accounting systems
- Digital clock circuits
- Exam questions in digital logic design
Converting BCD to Decimal
Split the BCD string into 4-bit groups, convert each group to its decimal digit, and concatenate. Example: 0100 0010 → 4 and 2 → 42.
Practice with Our BCD Converter
Our tool shows each digit's 4-bit group separately, making it easy to verify exam answers. Try converting 99 (1001 1001) or 1234 to see how multi-digit BCD works.