BCDtodecimal

BCDtodecimal refers to the process of converting a number encoded in binary coded decimal (BCD) into a standard base-10 decimal numeral. In BCD, each decimal digit is represented by a four-bit pattern, typically using the 8421 coding in which the patterns 0000 through 1001 map to the digits 0–9.

Common representations include packed BCD, where two decimal digits are stored per byte as two 4-bit nibbles, and unpacked BCD, where each decimal digit occupies its own byte. There are also variant codes such as 2421 or discussions of other weighted schemes, though 8421 is the most widely used standard. Some systems use sign nibble or dedicated sign codes for representing negative numbers.

To convert from BCD to decimal, the usual procedure is to decode each 4-bit nibble to its corresponding decimal digit and then assemble the digits in their proper order. For packed BCD, each nibble is translated and the digits are concatenated from most significant to least significant. If a nibble contains an invalid value (1010–1111), the result may be flagged as an error or treated according to the specific system’s conventions. In some contexts, a separate sign handling step may be needed.

Practical use of BCD-to-decimal conversion appears in calculators, digital displays, financial instruments, and embedded systems where precise decimal digit representation is important. While BCD simplifies digit-by-digit display and arithmetic, it is less storage-efficient than pure binary and can incur conversion overhead in software or hardware. See also BCD, decimal numbers, and 8421 code.