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 — Decimal, Hex, Octal

Binary Coded Decimal (BCD) is a class of binary encoding scheme where each decimal digit is represented by a fixed number of binary bits — most commonly 4 bits per digit. The decimal number 45 becomes 0100 0101 in 4-bit BCD. BCD is widely used in systems that display decimal numbers directly, such as digital clocks, cash registers, and calculators.

How BCD Works

In standard BCD (also called 8421 BCD), each decimal digit 0–9 is represented as its 4-bit binary equivalent. For example: 0 = 0000, 5 = 0101, 9 = 1001. The digits 1010 through 1111 (10–15 in binary) are invalid in BCD and must never appear. Multi-digit numbers are represented by concatenating the 4-bit groups for each digit.

BCD vs Binary

BCD preserves individual decimal digits, making display and rounding straightforward
BCD is less storage-efficient than pure binary (uses up to 20% more bits)
BCD arithmetic avoids the floating-point rounding errors that affect binary arithmetic
Pure binary is faster for arithmetic; BCD is preferred for human-readable output

Frequently Asked Questions

What is 8421 BCD?

8421 BCD is the most common BCD format. The weights of the four bits in each group are 8, 4, 2, and 1 — matching standard binary bit weights.

Why is BCD used in financial systems?

BCD avoids the rounding errors inherent in IEEE 754 binary floating-point. Financial calculations require exact decimal representation — e.g., $0.10 cannot be represented exactly in binary.

BCD Converter online

Convert between Binary Coded Decimal and decimal, hex, or octal — runs in your browser

How BCD Works

BCD vs Binary

Frequently Asked Questions

What is 8421 BCD?

Why is BCD used in financial systems?