bcd code calculator - Aaron Graves, PhDude Replica

Interactive BCD Code Calculator

Convert decimal numbers to 8421 BCD and convert BCD back to decimal instantly.

Decimal Number (0-9 digits, any length)

BCD Bits (4-bit groups)

Tip: BCD input may include spaces or commas. Each 4-bit nibble must represent a decimal digit from 0 to 9 (0000 to 1001).

What Is BCD Code?

BCD stands for Binary-Coded Decimal. Instead of converting an entire decimal number directly into pure binary, BCD converts each decimal digit into a 4-bit binary value.

For example, decimal 59 in BCD is:

5 → 0101
9 → 1001
So BCD = 0101 1001

In standard 8421 BCD, valid digit codes are only 0000 through 1001. Values 1010 to 1111 are invalid for decimal digits.

How to Use This Calculator

1) Decimal → BCD

Enter a decimal number (digits only), then click Convert Decimal → BCD. The tool returns:

BCD grouped by 4 bits
Continuous packed bit stream
Packed BCD bytes in hexadecimal

2) BCD → Decimal

Paste BCD bits using groups of 4 (spaces optional), then click Convert BCD → Decimal. The tool checks each nibble for validity before converting.

Why BCD Is Still Useful

BCD is common in places where decimal accuracy and human-readable digits are important:

Digital clocks and calculators
Financial and accounting hardware
7-segment display drivers
Legacy embedded systems

While pure binary is more memory efficient, BCD can simplify decimal display logic and reduce decimal rounding issues in specific applications.

Packed vs. Unpacked BCD

Unpacked BCD

Each decimal digit uses one full byte (usually upper nibble is 0000). Easier to process, uses more memory.

Packed BCD

Two decimal digits are stored in one byte (one digit in each nibble). More compact and common in low-level data formats.

Worked Examples

Example A: 2026 to BCD

2 → 0010
0 → 0000
2 → 0010
6 → 0110

Result: 0010 0000 0010 0110

Example B: 0101 1001 to Decimal

0101 → 5
1001 → 9

Result: 59

Common Input Errors

Using non-binary characters (anything besides 0 and 1)
Bit count not divisible by 4
Using invalid digit nibbles like 1100

This calculator validates these cases and shows a clear error message so you can correct the input quickly.

Quick FAQ

Is BCD the same as binary?

No. Binary converts the whole number, while BCD converts each decimal digit separately.

Can BCD represent negative numbers?

Standard 8421 BCD represents digits 0–9. Signed decimal formats exist, but they require extra conventions not covered by basic BCD.

Why are there invalid 4-bit patterns in BCD?

Because 4 bits can represent 16 values, but decimal digits need only 10 values. The extra six patterns are unused in standard 8421 BCD.