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 sets the carry flag on borrow while some machines (such as the 6502 and the PIC) instead resets the carry flag on borrow (and vice versa).
Read more about Carry Flag: Uses, Carry Flag Vs. Borrow Flag
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—Propertius Sextus (c. 50–16 B.C.)
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—Benjamin Harrison (1833–1901)