\begin{definition}[Definition:Classical Algorithm/Primitive Subtraction]
The '''primitive''' operation for '''subtraction''' 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 $z = -1$.
Subtraction of $y$ from $x$ with $z$ gives a $1$-digit '''difference''' $d$ and a $1$-digit '''carry''' $c$ such that:
{{begin-eqn}}
{{eqn | l = d
      | r = \paren {x - y + z} \pmod b
}}
{{eqn | l = c
      | r = \floor {\dfrac {x - y + z} b}
}}
{{end-eqn}}
In this context, the carry digit is often referred to as a '''borrow'''.
\end{definition}