8421

8421 refers to a binary-coded decimal (BCD) representation in which each decimal digit is encoded by a four-bit group with weights 8, 4, 2, and 1. In standard 8421 BCD, the patterns 0000 through 1001 represent the decimal digits 0 through 9; patterns 1010 through 1111 are invalid for representing digits. Thus a decimal number such as 38 would be encoded as two nibbles: 0011 for 3 and 1000 for 8.

The 8421 code is valued for its simple decimal interpretation: the value of each nibble is recovered by summing the weights of the set bits. Because only the digits 0–9 are valid in each nibble, arithmetic in BCD can be implemented with dedicated logic or with binary adders followed by decimal corrections. A common correction rule after addition is to add 0110 (decimal 6) to a nibble that results in a value greater than 9 or produces a carry, propagating carries as needed. This underpins BCD adders, subtractors, and related circuits.

Applications of 8421 BCD include digital clocks, calculators, digital readouts, and display drivers for seven-segment displays. The code is also used in microprocessors and digital systems that interface with human-readable decimal data, because its weights align with straightforward decimal representation.

Relation to other codes: 8421 is one of several BCD encodings. It is often contrasted with Excess-3 or other weighted codes; while 8421 is widely used for its decimal-friendly structure, alternative schemes exist for specific hardware or encoding requirements.