1. DR.S & S.S GHANDHY ENEGINEERING COLLAGE SUBJECT:DIGITAL ELECTRONICS

2. 130230111001-ADITI AGGRAWAL 130230111007-AYUSHI MEHTA 130230111027-KRISHNA PATEL 130230111031-NIKITA PATEL 130230111043-ROSHNI TAILOR 130230111046-RIYA SHAH SUBMITED TO:

3. STATE MACHINES  DEFINITION:  A State machine or finite machine(FSM) or a sequential machine is a system that can be described in terms of a set of states that the system may enter into.  A FSM has a set of inputs,and a set of outputs.the next state of FSM depends on the present state and inputs.the outputs also depends on the present state and inputs.

4.  GENERAL MODEL OF SEQUENTIAL MACHINE

5. The output of a sequential machine depends on the present state as well as the past state. The present state is stored in the memory elements.The present states are applied to the combinational cicuit alongwith the external inputs. The outputs and the next state of the sequential machine are decided by the external inputs and the present state.

6.  C LASSIFICATION OF STATE MACHINES : 1. On the basis of block. 2. On the basis of model used.  CLASSIFITION ON THE BASIS OF CLOCK: 1.Synchronous state machines 2.Asynchronous state machines 3.Machine synchronous state machine  CLASSIFITION OF STATE MACHINES BASED ON MODEL TYPE: 1.Moore machine:Depends on the present state of flip flop. 2.Mealy machine:Depends on the present state of flip flop and the external inputs.

7.  M OORE MACHINE :

8. The combinational circuts C1 on the inputs side is called as the next state decoder.The external inputs and the feedback singals from the memory elements are applied to this combinational circuit.C1 is also called Input Forming Logic(IFL). The outputs of the memory elements are applied to another combinational circuits C2 which is also called as output decoder.C2 is called as Output Forming Logic(OFL).

9.  MEALY MACHINES:

10.  A PPLICATIONS OF THE STATE MACHINES : 1.Motor controllers 2.Traffice lights controller 3.Vending machines 4.Sequence generaters 5.Sequence detectors and many more….

11.  S TATE MACHINE NOTATIONS : 1.Input variable 2.Output variable 3.State variable:As the output of the flip flops 4.Excitation variable:As the inputs of the memory(flip flop). 5.State:The state of a sequential machines is dependent on the content of memory. The relation between state variable and state is: y=2^x y=maximum number of possible states x=number of state variables

12. PRESENT STATE:The status of all state variable at any instant say “t” before the application of next clock edge is called a present state. NEXT STATE:The status of all state variable at the same time instant say “t+1” after the application of clock edge is called as next state.

13.  E XCITATION TABLE OF SR FLIP FLOP : Present state of Q output Next state of Q output Sn input Rn output CASE 1000 x CASE 20110 CASE 31001 CASE 411 x0

14. EXCITATION TABLE OF D FLIP FLOP: EXCITATION TABLE OF JK FLIP0 FLOP: OutputInput Present stateNext stateDn 000 011 100 111 OutputInput Present state Next stateJnKn 000x 011x 10x1 11x0

15. EXCITATION TABLE OF T FLIP FLOP: OutputInput Present stateNext stateTn 000 011` 101 110

16.  S TATE TABLE : Present state Next stateOutput Y X=0X=1X=0X=1 Qa Qb 0 0 100 1 0 100 1 01 0 01 1 10

17. The basic element of a sequential circuit is a flip flop.The outputs Qa,Qb,…..etc of such flip flops will be used as state inputs to a sequential circuit.they are also called as state variable. In addition to this “x” represents an external input and Y represents the output of the sequential circuit. Y will be dependent on the state variables and the external input x.

18. S TATE DIAGRAM :

19. The circle represents the present state.the arrows between the circles define the state trastion say from 00 to 01 or 01 to 11. A directed line connecting the same circle indicates that next state is same as the present state. The lining joining the circles are labeled with a pair of binary numbers with a “/” in between.for example the line joining 00 and 01 is labeled as 1/0.

20. THANK YOU