Definition:Classical Algorithm/Primitive Division

Definition
The primitive operation for division which can be used in the classical algorithms is defined as follows. Let $y$ be a $1$-digit integer.

Let $x$ be a $2$-digit integer $x_1 b + x_2$, where $x_1$ and $x_2$ are $1$-digit integers.

Suppose $x_1 \ge y$.

Then division of $x_1$ by $y$ gives a $1$-digit quotient $q$ and a $1$-digit remainder $r$, which is used as a carry, such that:

Suppose $x_1 < y$.

Then division of $x = x_1 b + x_2$ by $y$ gives a $1$-digit quotient $q$ and a $1$-digit remainder $r$, which is used as a carry, such that: