The Grid
Location arithmetic uses a square grid where each square on the grid represents a value. Two sides of the grid are marked with increasing powers of two. Any inner square can be identified by two numbers on these two sides, one being vertically below the inner square and the other to its far right. The value of the square is the product of these two numbers.
| 32 | ||||||
| 16 | ||||||
| 8 | ||||||
| 32 | 4 | |||||
| 2 | ||||||
| 1 | ||||||
| 32 | 16 | 8 | 4 | 2 | 1 |
For instance, the square in this example grid represents 32, as it is the product of 4 on the right column and 8 from the bottom row. The grid itself can be any size, and larger grids simply permit us to handle larger numbers.
Notice that moving either one square to the left or one square up doubles the value. This property can be used to perform binary addition using just a single row of the grid.
Read more about this topic: Location Arithmetic