\begin{definition}[Definition:Classical Algorithm/Primitive Multiplication]
The '''primitive''' operation for '''multiplication''' which can be used in the classical algorithms is:
Multiplication of '''two''' $1$-digit integers $x$ and $y$ gives a $1$-digit '''product''' $p$ and a $1$-digit '''carry''' $c$ such that:
{{begin-eqn}}
{{eqn | l = p
      | r = x \times y \pmod b
}}
{{eqn | o = 
}}
{{eqn | l = c
      | r = \dfrac {x \times y - p} b
}}
{{end-eqn}}
\end{definition}