A **half-carry flag** (also known as an **auxiliary flag** or **decimal adjust flag**) is a condition flag bit in the status register of many CPU families, such as the Intel 8080, Zilog Z80, the x86, and the Motorola 68000 series, among others. It indicates when a carry or borrow has been generated out of the least significant four bits of the accumulator register following the execution of an arithmetic instruction. It is primarily used in decimal (BCD) arithmetic instructions.

Normally, a processor that utilizes binary arithmetic (which includes almost all modern CPUs) will add two 8-bit byte values according to the rules of simple binary addition. For example, adding 25_{16} and 48_{16} produces 6D_{16}. However, for binary-coded decimal (BCD) values, where each 4-bit nibble represents a decimal digit, addition is more complicated. For example, adding the decimal value 25 and 48, which are encoded as the BCD values 25_{16} and 48_{16}, the binary addition of the two values produces 6D_{16}. Since the lower nibble of this value is a non-decimal digit (D), it must be adjusted by adding 06_{16} to produce the correct BCD result of 73_{16}, which represents the decimal value 73.

0010 0101 25
+ 0100 1000 48
-----------

** 0110 1101 6D**,

*intermediate result*
+ 0110 06,

*adjustment*
-----------

** 0111 0011 73**,

*adjusted result*
Likewise, adding the BCD values 39_{16} and 48_{16} produces 81_{16}. This result does not have a non-decimal low nibble, but it does cause a carry out of the least significant digit (lower four bits) into the most significant digit (upper four bits). This is indicated by the CPU setting the half-carry flag. This value must also be corrected, by adding 06_{16} to 81_{16} to produce a corrected BCD result of 87_{16}.

0011 1001 39
+ 0100 1000 48
-----------

** 1000 0001 81**,

*intermediate result*
+ 0110 06,

*adjustment*
-----------

** 1000 0111 87**,

*adjusted result*
Finally, if an addition results in a non-decimal high digit, then 60_{16} must be added to the value to produce the correct BCD result. For example, adding 72_{16} and 73_{16} produces E5_{16}. Since the most significant digit of this sum is non-decimal (E), adding 60_{16} to it produces a corrected BCD result of 145_{16}. (Note that the leading 1 digit is actually a carry bit.)

0111 0010 72
+ 0111 0011 73
-----------

** 1110 0101 E5**,

*intermediate result*
+ 0110 60,

*adjustment*
-----------

**1 0100 0101 145**,

*adjusted result*
Summarizing, if the result of a binary addition contains a non-decimal low digit or causes the half-carry flag to be set, the result must be corrected by adding 06_{16} to it; if the result contains a non-decimal high digit, the result must be further corrected by adding 60_{16} to produce the correct final BCD value.