An ALU uses the same width for the operands and the sum of an addition operation. Let us assume this width if n bits. The question is: what do we do with kn-1?
We cannot store this bit in a destination, as the destination (be it memory or register) is only as wide as the operands. This carry is known simply as the “carry” bit of the ALU. While it is not stored in the sum, it is still “latched” in an ALU, which means an ALU can retain the state of this most significant carry bit from one computation to the next. We will see later, perhaps in another module, how this latching of the most significant carry bit is useful.