Binary Coded Decimal (BCD) Converter – 8421 BCD in 3 Easy Steps
BCD Converter
Use this binary coded decimal converter to translate decimal numbers to 8421 Binary Coded Decimal with real-time visual mapping.
Use this free binary coded decimal converter to turn decimal numbers into 8421 BCD and BCD back into decimal. Type a number or a string of 4-bit groups, and the tool converts it instantly, shows each digit mapped to its own nibble, and warns you if a group is not valid BCD.
Quick answer
Binary coded decimal (BCD) stores each decimal digit as its own 4-bit binary group, called a nibble. 25 becomes 0010 0101, and 1987 becomes 0001 1001 1000 0111. Only 0000 to 1001 (0–9) are valid; 1010 to 1111 are not used in standard 8421 BCD.
Table of Contents
Normal binary converts the whole number at once, so 25 is 11001. BCD keeps the decimal digits separate, which makes it easy to drive seven-segment displays, store money values exactly and read numbers back without rounding.
This binary coded decimal converter shows the digit-by-digit mapping, so it is also a handy learning aid for digital electronics and computer science classes.
How 8421 BCD Works
- Take each decimal digit separately.
- Write it as a 4-bit binary number using weights 8, 4, 2 and 1.
- Join the nibbles in the same order as the digits.
- To decode, split the bits into groups of 4 and turn each group back into a digit.
8421 BCD Reference Table
| Decimal | BCD | Decimal | BCD |
|---|---|---|---|
| 0 | 0000 | 5 | 0101 |
| 1 | 0001 | 6 | 0110 |
| 2 | 0010 | 7 | 0111 |
| 3 | 0011 | 8 | 1000 |
| 4 | 0100 | 9 | 1001 |
BCD vs Pure Binary
| Decimal | 8421 BCD | Pure binary |
|---|---|---|
| 25 | 0010 0101 | 11001 |
| 493 | 0100 1001 0011 | 111101101 |
| 1987 | 0001 1001 1000 0111 | 11111000011 |
BCD uses more bits than pure binary, but each group lines up with one decimal digit, which is why it is still used in clocks, calculators and financial hardware.
How to Use the Binary Coded Decimal Converter
Step 1: Convert a Decimal Number to BCD
Type a whole number in Decimal Number (Base 10). For 1987, the Binary Coded Decimal box shows 0001 1001 1000 0111, and the Visual Nibble Mapping lines up 1, 9, 8 and 7 with their 4-bit codes.
Step 2: Convert BCD Back to Decimal
Type BCD bits into the second box, with or without spaces. 0100 1001 0011 converts back to 493, and the mapping shows 4, 9 and 3 above their nibbles.
Step 3: Spot Invalid Nibbles With the Reference Table
If you enter a group above 1001, such as 1010 0001, the box turns red with the message that standard 8421 BCD only allows 0000 to 1001. Compare your bits with the 8421 BCD Reference Table and press Clear Fields to try again.
Where BCD Is Used
- Seven-segment displays in clocks, meters and timers.
- Real-time clock chips that store hours, minutes and seconds in BCD.
- Calculators and point-of-sale systems that need exact decimal values.
- Mainframe and COBOL packed decimal formats for money.
- Digital logic and computer architecture courses.
Packed vs Unpacked BCD
Packed BCD stores two digits in one byte, for example 25 as 0010 0101. Unpacked BCD uses a full byte per digit, so 25 is 0000 0010 0000 0101. This converter shows the packed nibble form, which is the most common.
BCD Addition and the +6 Correction
When two BCD digits add up to more than 9, the 4-bit result is not valid BCD. Hardware fixes this by adding 6 (0110) and carrying 1 to the next digit. For example, 7 + 5 = 12: binary gives 1100, which is invalid, so adding 0110 gives 1 0010, written as 0001 0010, which is 12 in BCD.
This is why processors have a decimal adjust instruction. Try the result in the binary coded decimal converter to confirm that 0001 0010 decodes to 12.
More number tools: the Base32 Encoder Decoder, the NATO Phonetic Alphabet Translator and the Morse Code Converter.
Frequently Asked Questions
What is binary coded decimal?
It is a way of writing numbers where each decimal digit is stored as its own 4-bit binary group.
How do I convert 25 to BCD?
Convert each digit separately: 2 = 0010 and 5 = 0101, so 25 = 0010 0101.
Why is 1010 invalid in BCD?
1010 is 10 in binary, which is not a single decimal digit. Standard 8421 BCD only uses 0000 to 1001.
Is BCD the same as binary?
No. Pure binary converts the whole number, while BCD converts each digit. 25 is 11001 in binary but 0010 0101 in BCD.
Why is it called 8421 BCD?
The four bits in each nibble have place values of 8, 4, 2 and 1.
Is my data saved?
No. The binary coded decimal converter runs in your browser and nothing is stored.