Definition:Classical Algorithm/Primitive Addition

Definition
The primitive operation for addition which can be used in the classical algorithms is: Let $x$ and $y$ be $1$-digit integers.

Let $z$ be a carry digit such that either $z = 0$ or $z = 1$.

Addition of $x$, $y$ and $z$ gives a $1$-digit sum $s$ and a $1$-digit carry $c$ such that: