1. FSM examples

2. Odd Parity Checker
Design a circuit that detects whether there are an odd number of 1s in an input bit stream. Assume that the rate of inputs is 1 every clock cycle.
We have input bit stream
Next State will depend on current state as well as the current input

3. Odd Parity Checker- State Graph

4. Odd Parity Checker- State Table
Even number of ones = State S0 = 1’b0
Odd Number of Ones = State S1 = 1’b1
Present State
Input
Next State
Output 1

5. Odd Parity Checker – Next State Logicin
Present State 1 1 1 1

6. Odd Parity Checker - Circuit

7. Odd Parity Checker – Verilog Code
module odd_parity( in, clk, reset, Out); input in, clk, reset; output Out; reg state, next_state; wire Out; parameter S0 = 1’b0, S1 = 1’b1;

8. Odd Parity Checker – Verilog Code
// Next State Logic (in or state or reset) begin if( reset ==0) next_state =S0; else case(state) S0: begin if(in==1) next_state = S1; else next_state = S0; end S1: begin if(in ==1) next_state =S0; else next_state = S1; endcase

9. Odd Parity Checker – Verilog Code
// State Register (posedge clk or negedge reset) begin if(reset==0) state <=S0; else state <= next_state; end // Output Logic assign Out = state;

10. State Machine Example
X=1

11. State Machine Example – State TableQ0 Q1 X N0 N1 1

12. State Machine Example – Circuit Realisation
Q0 Q1 00 01 11 10 x 1 1 N1
Q0 Q1 x 00 01 11 10 1 1
N1 = x

13. State Machine Example – Verilog Code
module state_machine(x, clk, reset, Out); input x, clk, reset; output[1:0] Out; reg[1:0] state, next_state; wire[1:0] Out; parameter S0 = 2’b00, S1 = 2’b01, S2 = 2’b10, S3 = 2’b11;

14. State Machine Example – Verilog Code
// Next State Logic (x or state or reset) begin if(reset ==0) next_state =S0; else case(state) S0: begin if(x==0) next_state = S0; else next_state = S1; end S1: begin if(x==0) next_state = S2; else next_state = S3; S2: begin S3: begin endcase

15. State Machine Example – Verilog Code
//State Register Logic (posedge clk or negedge reset) begin if(reset == 0) state <= S0; else state <= next_state; end //Output Logic assign Out = state;