1. Motivation
Combinational logic functions can be represented, and defined, by truth tables.
Sequential logic function cannot, because their behavior depends upon both the state of their inputs and their current state.
Implementing the control logic for a CPU will require using sequential logic functions, and we need a tool to express and model those functions mathematically.
Computer Science Dept Va Tech January 2006
©2006 McQuain WD

2. Finite State Machine A finite state machine (FSM) is…
- a finite set of states Q = {S0, S1, , SN}, and
- a set of possible input values I = {i0, i1, , iK}, and
- a set of possible output values O = {o0, o1, , oM}, and
- a next state function F:QxIS, and
- an output function G:QxIO
The next state function maps the current inputs and the current state the next state of the FSM.
The output function maps the current state and possibly the current inputs to a set of asserted outputs.
Computer Science Dept Va Tech January 2006
©2006 McQuain WD

3. Example
Here's a simple FSM representing a basic digital function. We have:
Q = {E, O}
I = {0, 1, end}
O = {'E', 'O'}
What's the next state function?
What does it DO? E O
start
halt 1
end/E
end/O
Computer Science Dept Va Tech January 2006
©2006 McQuain WD

4. Example: Parity Checker
Here's an application of the FSM from the previous slide:
Here's the next-state function for the previous slide.
Here's a bit-chucker to pass the bits to the next-state function.
Here's the memory element to store the current state.
Here's a counter to disable changes after 8 ticks
Computer Science Dept Va Tech January 2006
©2006 McQuain WD

5. Relationship to Hardware
Common design issues in hardware control can be efficiently represented and analyzed using FSMs.
Computer Science Dept Va Tech January 2006
©2006 McQuain WD