halfcarry

Half carry, or the half-carry flag, is a status indicator used in several 8-bit CPU architectures to signal a carry or borrow that occurs within the lower nibble of a byte (the lowest four bits) during arithmetic. In practice, it flags a carry from bit 3 to bit 4 in additions, or a borrow from bit 4 in subtractions. The exact behavior can vary by processor, but the common purpose is to assist binary-coded decimal (BCD) arithmetic and related low-nibble operations.

In addition, the half-carry flag is typically set when the sum of the low nibbles exceeds 0x0F. For example, adding 0x09 and 0x07 yields a low-nibble sum of 0x09 + 0x07 = 0x10, which requires a carry into the high nibble, so the half-carry flag is set. In subtraction, the flag is set when the low nibble borrow is needed, i.e., when the low nibble of the minuend is smaller than the low nibble of the subtrahend.

The half-carry flag is used by decimal adjust operations such as DAA (Decimal Adjust after Addition) in some architectures to convert binary results into valid BCD. It also participates in the broader flag behavior of instructions that perform addition or subtraction with carry (ADC/SBC on some CPUs), where the nibble-level carry information influences the final result and subsequent flag states.

Architectures that implement a half-carry concept include the Z80 family, the Intel 8080 lineage, the Game Boy’s LR35902 CPU, and microcontrollers such as the 8051 (where a related auxiliary carry flag serves a similar role). Modern CPUs without BCD support may omit a dedicated half-carry flag.