CE Optimized State Machines
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1 C 1911 Optimized State Machines
2 Un-used states o we care about un-used states? YS! Start-up Bit errors 2 tj
3 Un-used states Mod 5 counter reset tj
4 Un-used states Mod 5 counter What happens if an event causes the state to become corrupted reset tj
5 Un-used states Mod 5 counter Recovery solution reset tj
6 Un-used states Mod 5 counter Recovery solution reset tj
7 Un-used states Mod 5 counter self starting reset not required reset may not work in simulation 7 tj
8 Redundant states lead to more logic than necessary 2 States are equivalent if Outputs are the same Transition to the same next state if the inputs are the same 8 tj
9 Informal analysis Redundant states lead to more logic than necessary 3 state variables 3 output bits x y A 100 x+y x y x+y B 010 y x y x y C y 101 y x y 9 tj
10 Informal analysis States and have the same output (101) both go to C when y is true both go to when y is true Combine and 10 tj
11 Informal analysis Redundant states lead to more logic than necessary 3 state variables 2 state variables 3 output bits re-encoded to 2 bits x y A x+y x y x+y B 010 y x x y C y 11 x y 11 tj
12 Successive Partitions State Input Next State A 0 B A 1 C B 0 B 1 C 0 C 1 0 B 1 G 0 1 C 0 1 G 0 G 1 G State Output A 1 B 1 C G 0 State Input Next State Output A 0 B 1 A 1 C 1 B 0 1 B 1 1 C 0 0 C B 1 1 G C G 0 0 G 1 G 0 12 tj
13 Successive Partitions Partitions Next States Action P0 ABCG Identify states and outputs 13 tj
14 Successive Partitions Partitions Next States Action P0 ABCG Partition into sets with same outputs AB, CG 14 tj
15 Successive Partitions Partitions Next States Action P0 P1 In = 0 In = 1 AB BB CG ABCG CG CG AB, CG Identify next states based on current state and inputs 15 tj
16 Successive Partitions Partitions Next States Action P0 P1 In = 0 In = 1 AB BB CG ABCG CG CG Identify any groups of next states that are not part of an existing partition those groups by current state AB, CG CG and 16 tj
17 Successive Partitions Partitions Next States Action P0 P1 In = 0 In = 1 P2 In = 0 In = 1 AB BB CG AB BB CG ABCG CG CG CG CG AB, CG CG and Identify next states based on current state and inputs 17 tj
18 Successive Partitions Partitions Next States Action P0 P1 In = 0 In = 1 P2 In = 0 In = 1 AB BB CG AB BB CG ABCG CG CG CG CG Identify any groups of next states that are not part of an existing partition AB, CG CG and A and B those groups by current state 18 tj
19 Successive Partitions Partitions Next States Action P0 P1 In = 0 In = 1 P2 In = 0 In = 1 P2 In = 0 In = 1 A BB CG AB BB CG AB BB CG B ABCG CG CG CG CG CG CG AB, CG A and B CG and 19 tj A and B Identify next states based on current state and inputs
20 Successive Partitions Partitions Next States Action P0 P1 In = 0 In = 1 P2 In = 0 In = 1 P2 In = 0 In = 1 ABCG AB, CG AB CG Identify any groups of next states that are not BB A and B part of an existing partition CG CG CG and AB those groups by CG current state BB CG CG A BB CG B CG CG A and B No more reduction 20 tj
21 Successive Partitions Partitions Next States Action P0 P1 In = 0 In = 1 P2 In = 0 In = 1 P2 In = 0 In = 1 A BB CG AB BB CG AB BB CG B ABCG CG CG CG CG CG CG Pfinal A B CG AB, CG A and B CG and 21 tj A and B No more reduction
22 Successive Partitions State Input Next State Output A 0 B 1 7 states 4 states A 1 C 1 B 0 1 B 1 1 C 0 0 C B 1 1 G C G 0 0 G 1 G 0 State Input Next State Output A 0 B 1 A 1 CG 1 B 0 A 1 B 1 1 CG 0 0 CG 1 CG 0 0 CG 0 1 A 0 State Input Next State Output P 0 Q 1 P 1 R 1 Q 0 P 1 Q 1 S 1 R 0 S 0 R 1 R 0 S 0 R 0 S 1 P 0 22 tj
23 Implication Chart A B C G A B C G 23 tj
24 Implication Chart compare pairs of states If outputs are different out box A B C G A B C G 24 tj
25 Implication Chart write in the implicants to all empty boxes The two states would be the same I the implicants are the same A B C G B- C- B-B C-G B- -G - C G States A and B would be the same ONLY if B and are the same and C and are the same - C- - C-G - -G A B C G 25 tj
26 Implication Chart Traverse the structure and out any boxes whose implicants are already d out This indicates the implicant is not true A B C G B- C- B-B C-G B- -G - C G - C- - C-G - -G A B C G 26 tj
27 Implication Chart Traverse the structure and out any boxes whose implicants are already d out This indicates the implicant is not true A B C G B- C- B-B C-G B- -G - C- - -G - C-G A B C G 27 tj
28 Implication Chart Traverse the structure and out any boxes whose implicants are already d out This indicates the implicant is not true A B C G B-B C-G - C- - -G - C-G A B C G 28 tj
29 Implication Chart Remaining un- d boxes indicate equivalent states A B C G B-B C-G - C- - -G A B - C-G A B C G CG 29 tj
30 Implication Chart State Input Next State Output A 0 B 1 7 states 4 states A 1 C 1 B 0 1 B 1 1 C 0 0 C B 1 1 G C G 0 0 G 1 G 0 State Input Next State Output A 0 B 1 A 1 CG 1 B 0 A 1 B 1 1 CG 0 0 CG 1 CG 0 0 CG 0 1 A 0 State Input Next State Output P 0 Q 1 P 1 R 1 Q 0 P 1 Q 1 S 1 R 0 S 0 R 1 R 0 S 0 R 0 S 1 P 0 30 tj
31 esign Process Circuit esign 1) Identify the states collectively these make a state variable 2) Identify the Inputs and Outputs 3) Assign values for each input/output (encoding) 4) Create a state transition diagram / table 5) Optimize the state transition table 6) Assign values for the state variable for each state (encoding) 7) Create truth tables for the combinational logic blocks in the machine model: next state, output 8) Minimize the next state and output equations using K-maps or Boolean Algebra techniques 9) raw the circuit schematic 10) Verify the solution 11) Build the physical circuit 12) Test the physical circuit to ensure correct operation esign Process HL 1) Identify the states collectively these make a state variable 2) Identify the Inputs and Outputs 3) Create a state transition diagram / table 4) Optimize the state transition table 5) Create the HL to match the state transition table 6) Choose an encoding scheme (or let the tool decide) 7) Synthesize the design 8) Verify the solution 9) Build the physical circuit 10) Test the physical circuit to ensure correct operation 31 tj
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