A Note on the Number of Internal Variable Assignments for Sequential Switching Circuits

Abstract
An important step in the synthesis of sequential switching circuits is the assignment of binary variable states to represent internal states of the circuit. A formula is derived here which indicates the number of different assignments which can be made for flow tables having a given number of rows. There are only three essentially different assignments possible for a four-row table, and there are 140 for a five-row table.

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