Talk:Digital Circuits/Finite State Machines

=Help Needed= I wrote what I know of finite state machines, transition tables, and state diagrams from a more general mathematics/computer science background in a fashion I thought applied to digital circuits, but I was actually reading through here in an attempt to learn about digital circuits, so I am uncertain as to its appropriateness for this context. Jay W. 10:56, 29 December 2006 (UTC)

Fact Check
User:139.168.29.22 wrote that:

A system that has "n" inputs can potentially go from any state to 2^n other states. (here)

This strikes me as false. A finite state machine with $$n$$ inputs could have only 1 state, its initial, with all combinations of those inputs generating a transition to the identical state. (For example: a 2-input AND gate acting as the function $$F(x) = xx^\prime$$.) If someone else thinks he was right, feel free to comment here about it, and we can see about adding it back in. &mdash;Jay W. 23:34, 22 January 2007 (UTC)

I think what that confusingly-brief sentence was trying to say was: Given a system with "n" inputs, the "branching factor" of any particular state is at most 2^n. For example, given a finite state machine with only 1 input, each state can transition to at most 2^1 = 2 other states (a binary tree). Certainly most real systems have a branching factor far, far less than 2^n -- any particular state goes to only a few other states, any particular input is ignored in most states.

It seems fairly obvious to me -- but it is obvious enough that we don't need to mention it to a new learner? --DavidCary 17:59, 13 July 2007 (UTC)