Carry flag

In computer processors the carry flag (usually indicated as the C flag) is a single bit in a system status (flag) register used to indicate when an arithmetic carry or borrow has been generated out of the most significant ALU bit position. The carry flag enables numbers larger than a single ALU width to be added/subtracted by carrying (adding) a binary digit from a partial addition/subtraction to the least significant bit position of a more significant word. It is also used to extend bit shifts and rotates in a similar manner on many processors (sometimes done via a dedicated X flag). For subtractive operations, two (opposite) conventions are employed as most machines set the carry flag on borrow while some machines (such as the 6502 and the PIC) instead reset the carry flag on borrow (and vice versa).

The carry flag is affected by the result of most arithmetic (and typically several bit wise) instructions and is also used as an input to many of them. Several of these instructions have two forms which either read or ignore the carry. In assembly languages these instructions are represented by mnemonics such as ADD/SUB, ADC/SBC (ADD/SUB including carry), SHL/SHR (bit shifts), ROL/ROR (bit rotates), RCR/RCL (rotate through carry), and so on. The use of the carry flag in this manner enables multi-word add, subtract, shift, and rotate operations.

An example is what happens if one were to add 255 and 255 using 8-bit registers. The result should be 510 which is 1_1111_1110 in binary, requiring 9 bits. The 8 least significant bits always stored in the register would be 1111_1110 binary (254 decimal) but since there is carry out of bit 7 (the eight bit), the carry is set, indicating that the result needs 9 bits. The valid 9-bit result is the concatenation of the carry flag with the result. Note that in an 8-bit two's complement interpretation, this operation is −1 + −1 and yields the correct result of −2, with no overflow, even if the carry is ignored.

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