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State Table and Excitation Table

Systematic methods for deriving the required input signals (excitation) needed to transition the circuit from a given current state to a desired next state.
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The statement of the theorem

Given a current state QQ and a desired next state QnextQ_{next}, the required input excitation XX must satisfy the Boolean equations derived from the state transition logic. The excitation table determines XX such that Qnext=f(Q,X)Q_{next} = f(Q, X). For a specific flip-flop, the required input XX is derived by solving the characteristic equation for XX: X=f−1(Qnext,Q)X = f^{-1}(Q_{next}, Q) This process systematically maps (Q,Qnext)→X(Q, Q_{next}) \to X.