bcd

Binary-Coded Decimal (BCD) is a class of digital encoding schemes for decimal numbers in which each decimal digit is represented by a fixed number of binary bits. In the most common form, each decimal digit is encoded in four bits (a nibble), so a decimal digit 0–9 maps to binary 0000–1001. The bit patterns 1010–1111 are typically invalid in standard 8421 BCD, though some systems use them for special purposes.

The standard variant is 8421 BCD, where the four bits carry weights 8, 4, 2, and 1. A two-digit decimal value can be stored in one byte using packed BCD (two digits per byte), while unpacked BCD uses one full byte per digit. There are also alternative codes such as excess-3, where a decimal digit d is encoded as binary of d+3, and other non-8421 forms used in specific hardware or historical devices.

Arithmetic with BCD is performed per digit. When adding two BCD digits, a correction step is required if the result exceeds 9 or if there is a carry to the next digit; common implementations add 6 (0x06) to the nibble to re-align to decimal values. Subtraction can use ten’s complement methods. Conversions between BCD and binary or decimal strings are routine, and many processors offer dedicated instructions or libraries to assist.

Applications of BCD include digital displays (such as seven-segment displays), pocket calculators, and certain financial or embedded systems where decimal representation and precise decimal rounding are advantageous. Compared with pure binary, BCD is easier to read and display but less storage- and computation-efficient, making it a trade-off between human readability and machine efficiency.