Definition:Classical Algorithm/Primitive Addition/Base 10 Addition Table
Definition
The primitive addition operation for conventional base $10$ arithmetic of two $1$-digit integers can be presented as a pair of operation tables as follows:
- $\begin{array}{c|cccccccccc}
s & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline 0 & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ 1 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 0 \\ 2 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 0 & 1 \\ 3 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 0 & 1 & 2 \\ 4 & 4 & 5 & 6 & 7 & 8 & 9 & 0 & 1 & 2 & 3 \\ 5 & 5 & 6 & 7 & 8 & 9 & 0 & 1 & 2 & 3 & 4 \\ 6 & 6 & 7 & 8 & 9 & 0 & 1 & 2 & 3 & 4 & 5 \\ 7 & 7 & 8 & 9 & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ 8 & 8 & 9 & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ 9 & 9 & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \end{array} \qquad \begin{array}{c|cccccccccc} c & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 \\ 4 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 \\ 5 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 \\ 6 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 \\ 7 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 8 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 9 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \end{array}$
Sources
- 1998: Donald E. Knuth: The Art of Computer Programming: Volume 2: Seminumerical Algorithms (3rd ed.) ... (previous) ... (next): $4.3$: Multiple Precision Arithmetic: $4.3.1$ The Classical Algorithms