Binary Coded Decimal (BCD) encodes each decimal digit (0–9) as a 4-bit binary group. The decimal number 45 becomes 0100 0101 in BCD.

BCD is used in digital clocks, calculators, and systems where decimal accuracy matters, such as financial applications where floating-point errors must be avoided.

BCD Converter — Binary Coded Decimal

How to Use bcd-converter

Enter a decimal number in the input field.
The tool converts it to Binary Coded Decimal (BCD) instantly.
Also shows the equivalent binary, hex, and octal representations.
Toggle between 8421 BCD (standard) and Excess-3 BCD in the options.

Binary Coded Decimal (BCD) encodes each decimal digit (0–9) individually as a 4-bit binary group, rather than converting the entire number to binary. The decimal number 39 in BCD is 0011 1001 — the digit 3 as 0011 followed by the digit 9 as 1001. BCD is used in digital clocks, financial calculators, and seven-segment displays where decimal digits must be processed individually.

Why BCD Exists

Pure binary conversion of decimal numbers introduces decimal-to-binary rounding errors when working with values like 0.1 or 0.7. BCD avoids this by never leaving the decimal representation — each digit stays a digit throughout processing. Seven-segment LED displays drive segments from 4-bit BCD nibbles. Early pocket calculators and ATM hardware used BCD arithmetic for exact cent-level financial calculations.

8421 BCD (standard): each decimal digit as 4-bit binary
Excess-3 BCD variant (adds 3 to each digit before encoding)
Shows packed BCD alongside unpacked (space-separated nibbles)
Handles multi-digit numbers of any length

Frequently Asked Questions

What is the difference between BCD and binary?

Binary converts the entire number. BCD converts each decimal digit separately. Decimal 99 in binary is 1100011; in BCD it is 1001 1001 (two 4-bit groups: 9 and 9).

What is Excess-3 BCD?

Excess-3 (XS-3) adds 3 to each decimal digit before encoding in 4-bit binary. So digit 0 becomes 3 (0011), digit 9 becomes 12 (1100). This makes 9's complement easier to compute for decimal subtraction circuits.

Why can't BCD digits go above 9?

The 4-bit groups 1010 through 1111 (values 10–15) are illegal in BCD. They represent wasted bit patterns — an inherent inefficiency compared to pure binary encoding.

Where is BCD used today?

BCD appears in financial co-processors, smart card protocols (ISO 7816), telephony signalling (E.164 phone numbers in SS7), and the x86 BCD instruction set (DAA, DAS, AAA instructions).

See also Binary to Decimal, Hex to Binary, and the Gray Code converter.

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