BCD Converter: Translate Decimal to Binary Coded Decimal Instantly
Learn how Binary Coded Decimal (BCD) works and convert between decimal and 8421 BCD — packed, unpacked, and compared to pure binary — with the free online BCD Converter.
Table of Contents
Binary Coded Decimal (BCD) sits at the intersection of human-readable numbers and machine-level encoding. Digital clocks, seven-segment displays, and many financial computing systems rely on this scheme, in which each decimal digit is stored as its own 4-bit group. Yet converting between decimal and BCD by hand is tedious and error-prone: one misplaced nibble and the whole value changes.
The free BCD Converter does this work instantly. It converts decimal numbers to 8421 BCD in both packed and unpacked form, decodes BCD bit strings back to decimal, and shows the pure binary equivalent alongside so you can see exactly how the two encodings differ. Everything runs entirely in your browser — no signup, no installation, and no data leaving your machine.
Whether you are debugging embedded firmware, studying digital electronics, or verifying packed-decimal data from a legacy system, this guide explains how BCD works and how to convert it confidently.
Why Use the BCD Converter?
- Two-way conversion in one place. Switch between decimal → BCD and BCD → decimal without juggling tools or doing hand arithmetic.
- Packed and unpacked output at once. Every encoding returns both the continuous packed string (e.g. 01000111) and the nibble-separated unpacked form (e.g. 0100 0111).
- Built-in binary comparison. The tool also displays the pure binary equivalent, making it easy to see why 47 is 101111 in binary but 0100 0111 in BCD.
- Strict input validation. Decoding rejects non-binary characters, lengths that are not multiples of 4, and invalid nibbles (1010–1111) that have no meaning in 8421 BCD.
- Free, private, and instant. No account, no installation — the converter runs entirely client-side, so your inputs never leave your browser.
Key Features
| Feature | What You Get |
|---|---|
| Decimal → BCD mode | Encode any decimal number into 8421 BCD, digit by digit |
| BCD → Decimal mode | Decode a bit string back to decimal with full validation |
| Packed BCD output | Continuous bit string, e.g. 01000111 for 47 |
| Unpacked BCD output | Nibble-separated format, e.g. 0100 0111 for 47 |
| Binary comparison | Pure binary equivalent shown alongside for contrast |
| Input validation | Bits must be 0/1, length a multiple of 4, each nibble ≤ 9 |
| Free and private | No signup; runs entirely in the browser |
A few details worth highlighting:
- Both BCD layouts from a single input. Packed BCD is what hardware registers and mainframe formats typically store; unpacked is what documentation and debug output usually show. Getting both at once removes any ambiguity about format.
- The binary comparison prevents a classic mistake. BCD and pure binary look deceptively similar, so the side-by-side view makes the difference concrete instead of abstract.
How to Use
- Open the tool. Go to the BCD Converter — it loads instantly in any modern browser.
- Choose your direction. Select decimal → BCD to encode a number, or BCD → decimal to decode a bit string.
- Enter your value. Type a decimal number such as 47, or a BCD bit string such as 01000111.
- Read the results. Decimal input returns packed BCD, unpacked BCD, and the pure binary equivalent; BCD input returns the decoded decimal value.
- Copy what you need. Grab any output and paste it straight into your code, schematic notes, or homework.
Understanding BCD: How 8421 Encoding Works
BCD encodes each decimal digit independently as a 4-bit group called a nibble. In the most common variant, 8421 code (also called natural BCD), the four bits carry the weights 8, 4, 2, and 1 — exactly like the first four positions of ordinary binary. The digit 5 becomes 0101 (4 + 1), and 9 becomes 1001 (8 + 1). The complete mapping:
| Decimal digit | BCD (8421) |
|---|---|
| 0 | 0000 |
| 1 | 0001 |
| 2 | 0010 |
| 3 | 0011 |
| 4 | 0100 |
| 5 | 0101 |
| 6 | 0110 |
| 7 | 0111 |
| 8 | 1000 |
| 9 | 1001 |
Packed vs unpacked. Written back to back, the nibbles form packed BCD: 47 becomes 01000111. Written separately, usually space-separated, they are unpacked BCD: 0100 0111. The bits are identical; only the presentation differs.
Why 1010–1111 are invalid. Four bits can form sixteen patterns, but BCD needs only ten. The six patterns from 1010 through 1111 correspond to no decimal digit, so they are invalid in 8421 BCD. That is why the converter rejects any nibble above 9 when decoding: 0100 1010 is not a BCD number at all.
BCD vs pure binary. BCD is not the binary representation of a number. Take 47: in pure binary it is 101111 (32 + 8 + 4 + 2 + 1), while in BCD it is 0100 0111 — the digit 4 as 0100, the digit 7 as 0111. BCD usually takes more bits, but it preserves every decimal digit explicitly, which makes conversion to human-readable form trivial and keeps decimal values exact.
Where BCD appears. BCD shows up wherever decimal digits meet digital hardware: seven-segment displays and their driver chips, digital clocks and BCD counters, financial and mainframe systems (including COBOL packed-decimal fields) where exact decimal arithmetic matters, and embedded controllers that read thumbwheel switches or drive display modules.
Practical Use Cases
Digital Display and Seven-Segment Driver Work
Seven-segment display drivers commonly accept BCD inputs and generate the segment patterns themselves. If you are wiring a BCD counter to a display or programming a driver IC, converting 47 to 0100 0111 tells you exactly what to present on two 4-bit ports.
Embedded Firmware Debugging
When a register dump shows 01000111, reading it as pure binary gives 71 — but if the register holds packed BCD, the true value is 47. Misreading BCD as binary is a classic firmware bug, and the converter's comparison view helps you spot it fast.
Learning Digital Electronics and Computer Engineering
Number-system coursework moves quickly, and hand-encoding dozens of values is where mistakes pile up. Students can check homework against the converter, see the nibble structure visually, and build intuition for rules — like the invalid nibbles — that trip up many exam answers.
Verifying Mainframe and COBOL Packed-Decimal Data
Legacy financial systems store numbers in packed-decimal formats where each nibble is one digit. When inspecting a hex dump or debugging a data file, decoding those nibble strings with the converter gives you a fast, reliable sanity check on the values you are looking at.
Best Practices
- Confirm which format you have. Confusing BCD with pure binary changes the value entirely — use the comparison view to be sure.
- Mind the nibble boundaries. Group bits in fours from the right; a length that is not a multiple of 4 means truncated or corrupted data.
- Treat 1010–1111 as errors. A nibble above 9 is not valid 8421 BCD — investigate the source rather than forcing an interpretation.
- Remember BCD is per-digit. Digits are encoded independently, with no carry or weighting across nibbles as in pure binary.
- Use unpacked output for documentation. Nibble-separated strings are far easier to read in comments, lab reports, and study notes.
- Verify round-trips. Encode a number, decode the result, and confirm you get the original back — a quick habit that catches transcription errors.
Start Converting with the BCD Converter
BCD is a small idea with outsized importance in displays, clocks, financial computing, and embedded systems — and hand conversion is exactly the kind of tedious work a tool should do for you. Open the BCD Converter, type a decimal number or a bit string, and get packed BCD, unpacked BCD, and the binary comparison instantly. It is free, runs entirely in your browser, and validates every input so you can trust the output.
Related Tools You Might Like
- Base Converter — Convert numbers between binary, octal, decimal, and hexadecimal.
- Bitwise Calculator — Perform AND, OR, XOR, NOT, and shift operations on binary values.
- Hex Viewer — Inspect data as hexadecimal with byte-level detail.
Happy converting!