state machine n.
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State Machine - PowerPoint PPT Presentation

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State Machine
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  1. State Machine • Another type of sequential circuit • Combines combinational logic with storage • “Remembers” state, and changes output (and state) based on inputs and current state

  2. 4 1 8 4 30 25 5 20 10 15 Combinational vs. Sequential • Two types of “combination” locks Combinational Success depends only onthe values, not the order in which they are set. Sequential Success depends onthe sequence of values (e.g, R-13, L-22, R-3).

  3. State • The state of a system is a snapshot ofall the relevant elements of the systemat the moment the snapshot is taken. • Examples: • The state of a basketball game can be represented bythe scoreboard. • Number of points, time remaining, possession, etc. • The state of a tic-tac-toe game can be represented bythe placement of X’s and O’s on the board.

  4. State of Sequential Lock • Our lock example has four different states,labelled A-D:A: The lock is not open, and no relevant operations have been performed. • B: The lock is not open, and the user has completed the R-13 operation. • C: The lock is not open, and the user has completed R-13, followed by L-22. • D: The lock is open. • (user has completed R-13, L-22 and then R-3)

  5. State Diagram • Shows states and actions that cause a transition between states.

  6. Definition of a Finite State Machine • A set of input events • A set of output events • A set of states • A function that maps states and input to output • A function that maps states and inputs to states (which is called a state transition function) • Must be complete • A description of the initial state • A finite state machine is one that has a limited or finite number of possible states. 

  7. Example 2: A Door Combination Lock entry code is the 4-bit sequence “0110” Partial Complete

  8. Example 3: Odd Parity Checker

  9. Why Finite State Machines (FSMs) • A FSM is simple and intuitive way of describing a system which has discrete dynamics (State Transition Diagrams). • An FSM is an “abstract machine.” That means that we use a mathematical description of the machine to reason about it without actually building it. • A FSM can be directly and unambiguously converted into a digital electronic circuits. 

  10. Step 1: Form the State Transition Table (STT) (NS)

  11. Step 2: Code STT in numbers (NS) (NS) 

  12. Step 3: Implement STT

  13. Step 3a: Next State Logic for 1 D-Latch Output Inputs NS= (~PS S) + (PS ~S)

  14. Step 3b: Output Logic Output Inputs R= PS

  15. Step 4: Implement Circuit

  16. The Clock • Frequently, a clock circuit triggers transition fromone state to the next. • At the beginning of each clock cycle,state machine makes a transition,based on the current state and the external inputs. • Not always required. In lock example, the input itself triggers a transition. “1” “0” One Cycle time

  17. Master-Slave Flipflop • A pair of gated D-latches, to isolate next state from current state. PS NS PS During 1st phase (clock=1),previously-computed statebecomes current state and issent to the logic circuit. During 2nd phase (clock=0),next state, computed bylogic circuit, is stored inLatch A.