1. TOPIC : State Tables UNIT 1: Modeling and Simulation Module 4 : Modeling Sequential Circuits

2. State Diagrams Used to give an abstract description of the behavior of a system. The behavior is analyzed and represented in series of events, that could occur in one or more possible states. Example:

3. State diagrams of various flip-flops

4. State Tables It is one of many ways to specify a state machine. It is essentially a truth table whose ◦ Inputs  actual inputs and the current state ◦ Outputs  actual outputs and the next state It is a table showing what state a state machine will move to, based on the current state and other inputs.

5. One-dimensional State Tables Similar to truth tables Columns  naming of states, inputs, outputs Rows  Different possible signals Left side  Inputs, Right side  Outputs ABCurrent State Next State Output 00S1S21 00 S10 01 S20 01 S11 10 S21 10 S11 11 S21 11 S10

6. Two-dimensional State Tables Two forms of arranging them. 1)Vertical dimension  current states, horizontal  events, cells  contain the next state if an event happens S: state, E: event, A: action, --: illegal transition Events State E1E1 E2E2....EnEn S1S1 --A y /S j ….-- S2S2 ….A x /S i....…. SmSm A z /S k --….--

7. Contd … 2) Vertical dimension  current states, horizontal  events, cells  contain the next state if an event happens S: state, E: event, A: action, -: impossible transition Next current S1S1 S2S2 ….SmSm S1S1 A y /E j --….-- S2S2 ….A x /E i …. SmSm --A z /E k ….--

8. Example of a State-Table Input State 10 S1S1 S1S1 S2S2 S2S2 S2S2 S1S1 Columns  possible inputs Rows  possible states One can observe that from one of the above representations, other representation can beFound.

9. Transformation to state diagram Draw the circles to represent the states given. For each of the states, scan across the corresponding row and draw an arrow to the destination state(s). Designate a state as the start state. Designate one or more states as accept state.