What is Binary-Coded Decimal?

BCD represents each decimal digit (0 through 9) with its own fixed 4-bit binary group, called a nibble. Unlike pure binary, the digits are kept separate, so 25 becomes 0010 0101 rather than 11001.

What is the difference between packed and unpacked BCD?

Packed BCD stores two decimal digits in one byte (one nibble each). Unpacked BCD uses a full byte per digit, with the high nibble unused or set to a fill value. This tool shows the packed nibble groups.

Why are nibble values above 1001 invalid in BCD?

Each BCD nibble can only encode the digits 0 through 9, so binary values 1010 (10) through 1111 (15) are not valid BCD codes. The decoder flags any nibble in that range as an error.

BCD appears in digital clocks, calculators, financial systems, and instrumentation where exact decimal representation matters and where converting to a seven-segment display is simpler with digit-aligned bits.

Does BCD waste space compared to binary?

Yes. BCD uses four bits per digit but a single nibble can represent values up to 15, so codes 10 to 15 go unused. Pure binary is more compact, but BCD avoids decimal rounding and simplifies digit display.

BCD (Binary-Coded Decimal) Converter

What Binary-Coded Decimal is

Binary-Coded Decimal (BCD) stores each decimal digit in its own 4-bit group called a nibble, using the standard 8-4-2-1 weighting. Rather than converting a whole number to pure binary, BCD keeps the decimal digits separate, which makes it easy to drive seven-segment displays and to perform exact decimal arithmetic in clocks, calculators, and financial hardware.

How it works

To encode, each decimal digit d (0–9) maps directly to its 4-bit binary value. The number 2026 becomes four nibbles:

2    0    2    6
0010 0000 0010 0110

To decode, the input bits are split into groups of four from the right. Each group is read with weights 8, 4, 2, 1 to recover one decimal digit. Any nibble whose value lands between 1010 (10) and 1111 (15) is invalid BCD, because those codes do not correspond to a single decimal digit, and the decoder reports the error instead of guessing.

Tips and notes

When decoding, make sure the bit string length is a multiple of four; the tool pads short groups on the left so you can spot a malformed input quickly. The packed view shown here places two digits per byte, which is the most common hardware layout. If you need unpacked BCD, simply prefix each nibble with a fill nibble such as 0000 or 1111 depending on your platform’s convention.