\begin{definition}[Definition:Classical Algorithm/Primitive Addition]
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:
{{begin-eqn}}
{{eqn | l = s
      | r = \paren {x + y + z} \pmod b
}}
{{eqn | l = c
      | r = \floor {\dfrac {x + y + z} b}
}}
{{end-eqn}}
\end{definition}