Overview

The following gives the positions in n-stage autonomous cellular automata of the type 150 cells necessary to produce a maximum-length sequence of 2 ⁿ ? 1 states. All remaining cells in the n-stage string of cells are the simpler type 90 cells. See Figure 3.21 of Chapter 3.

Only the type 150 cells are listed below. The entry 12 3 7, for example, represents a 12-stage CA, with a type 150 cell in stages 3 and 7. All remaining stages 1, 2, 4, 5, 6, 8, 9, 10, 11 and 12 are type 90 cells.

The method of generating this data may be found in References 1, 2. The listings below are not the only possible minimal cost (fewest number of type 150 cells) realisations, and alternatives are possible. One disadvantage with a minimal cost realisation is that if the number of stages, n, requires to be increased, or decreased, then the positions of the type 90 and 150 cells in the string of cells will almost always require changing. This may not be necessary with a nonminimal realisation, where it may be possible to add or take away stages in the string without altering the other 90 and 150 cells. Conversely, the most costly realisation would be to standardise on type 150 cells throughout, using them as type 90 circuits where required by disconnecting the Q _k exclusive-OR signal.