Definition:Classical Algorithm/Primitive Subtraction/Base 10 Subtraction Table

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Definition

The primitive subtraction operation for conventional base $10$ arithmetic on two $1$-digit integers can be presented as a pair of operation tables as follows:

$\begin{array}{c|cccccccccc} d & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline 0 & 0 & 9 & 8 & 7 & 6 & 5 & 4 & 3 & 2 & 1 \\ 1 & 1 & 0 & 9 & 8 & 7 & 6 & 5 & 4 & 3 & 2 \\ 2 & 2 & 1 & 0 & 9 & 8 & 7 & 6 & 5 & 4 & 3 \\ 3 & 3 & 2 & 1 & 0 & 9 & 8 & 7 & 6 & 5 & 4 \\ 4 & 4 & 3 & 2 & 1 & 0 & 9 & 8 & 7 & 6 & 5 \\ 5 & 5 & 4 & 3 & 2 & 1 & 0 & 9 & 8 & 7 & 6 \\ 6 & 6 & 5 & 4 & 3 & 2 & 1 & 0 & 9 & 8 & 7 \\ 7 & 7 & 6 & 5 & 4 & 3 & 2 & 1 & 0 & 9 & 8 \\ 8 & 8 & 7 & 6 & 5 & 4 & 3 & 2 & 1 & 0 & 9 \\ 9 & 9 & 8 & 7 & 6 & 5 & 4 & 3 & 2 & 1 & 0 \\ \end{array} \qquad \begin{array}{c|cccccccccc} c & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 2 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 3 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 \\ 4 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 \\ 5 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 \\ 6 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 \\ 7 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 \\ 8 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 9 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array}$


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