Definition:Classical Algorithm/Primitive Subtraction

Definition
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:

In this context, the carry digit is often referred to as a borrow.