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One-Hot Encoded Finite State Machines

One-Hot Encoded Finite State Machines. InA’. A. InA’. InA. D. B. Z. InA. InB. C. Z. InB’. Example State Machine. State A = 00 State B = 01 State C = 10 State D = 11. D Q. D Q. Example Machine Implementation. Q1. N1 = Q1•Q0’ + Q1’•Q0•InA N0 = Q1•Q0’•InB + Q1’•Q0’•InA

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One-Hot Encoded Finite State Machines

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  1. One-Hot EncodedFinite State Machines ECEn 224

  2. InA’ A InA’ InA D B Z InA InB C Z InB’ Example State Machine State A = 00 State B = 01 State C = 10 State D = 11 ECEn 224

  3. D Q D Q Example Machine Implementation Q1 N1 = Q1•Q0’ + Q1’•Q0•InA N0 = Q1•Q0’•InB + Q1’•Q0’•InA Z = Q1’•Q0 + Q1•Q0’ Q0’ N1 Q1 Q1’ Q0 InA CLK Q1 Q0’ InB N0 Q0 • Logic Used: • 9 gates • 21 gate inputs • 2 flip flops Q1’ Q0’ InA CLK Q1’ Q0 Z Q1 Q0’ ECEn 224

  4. Choose a Different Encoding • A=1000, B=0100, C=0010, D=0001 Because of the state encodings,there are many illegal states.This TT with all these input don’t cares is the result This is called a one-hot encoding. Only one state bit is on at a time ECEn 224

  5. One-Hot Encoding Results • Will require 4 flip flops • One per state • Call the current state bits A, B, C, and D • Call the next state bits NA, NB, NC, and ND InA’ A By inspection we see: NA = A•InA’ + B•InA’ + D NB = A•InA NC = B•InA + C•InB’ ND = C•InB Z = B + C InA’ InA D B Z InA InB C Z InB’ ECEn 224

  6. D Q D Q D Q D Q One-Hot Implementation A B InA’ NA NC B InA A C InA’ C InB’ D CLK CLK NB ND A C B D InA InB CLK CLK B • Logic Used: • 9 gates • 19 gate inputs • 4 flip flops Z C ECEn 224

  7. One-Hot Observations • Choosing a one-hot encoding results in many, many don’t cares in transition table • Minimization results in simpler IFL and OFL • Requires more flip flops • Can do one-hot design by inspection • Without using transition tables… ECEn 224

  8. Another One-Hot Example x’ A x y’z B y’z’ y C ECEn 224

  9. D Q D Q D Q State Encoding and Structure NA A With one-hot encoding, each state has its own flip flop. ‘A’ is the name of a state and it is the name of the wire coming out of the flip flop for state ‘A’. The same holds true for states ‘B’ and ‘C’ NB B NC C ECEn 224

  10. One-Hot Encodings By Inspection x’ When is A the next state? Look at the arcs entering state A NA = A•x’ + B•y’z + C A x y’z B y’z’ y C ECEn 224

  11. One-Hot Encodings By Inspection x’ When is A the next state? Look at the arcs entering state A NA = A•x’ + B•y’z + C A x y’z B y’z’ y C ECEn 224

  12. One-Hot Encodings By Inspection x’ When is A the next state? Look at the arcs entering state A NA = A•x’ + B•y’z + C A x y’z B y’z’ y C ECEn 224

  13. One-Hot Encodings By Inspection x’ When is A the next state? Look at the arcs entering state A NA = A•x’ + B•y’z + C A x y’z B y’z’ y C Similar reasoning leads to: NB = A•x + B•y’z’NC = B•y ECEn 224

  14. The Key Lock Problem – One-Hot Version There will be 6 flip flops One for each state ECEn 224

  15. Key Lock Input Forming Logic NA = (PUSHED’•A) + (ECNT3’•E) + (WAITDONE•F) + (LOCKED•D) NB = (PUSHED’•B)+(PUSHED•7•A) NC = (PUSHED’•C)+(PUSHED•8•B) ND = (LOCKED’•D)+(PUSHED•9•C) NE = (PUSHED•7’•A) + (PUSHED•8’•B) + (PUSHED•9’•C) NF = (ECNT3•E) + (WAITDONE’•F) ECEn 224

  16. Key Lock Output Forming Logic ERROR = ECEn 224

  17. Key Lock Output Forming Logic ERROR = E INC = ECEn 224

  18. Key Lock Output Forming Logic ERROR = E INC = (PUSHED•7’•A) + (PUSHED•8’•B) + (PUSHED•9’•C) CLRTIMER = ECEn 224

  19. Key Lock Output Forming Logic ERROR = E INC = (PUSHED•7’•A) + (PUSHED•8’•B) + (PUSHED•9’•C) CLRTIMER = ECNT3•E CLRCNTR = ECEn 224

  20. Key Lock Output Forming Logic ERROR = E INC = (PUSHED•7’•A) + (PUSHED•8’•B) + (PUSHED•9’•C) CLRTIMER = ECNT3•E CLRCNTR = (WAITDONE•F) + (LOCKED•D) UNLOCK = ECEn 224

  21. Key Lock Output Forming Logic ERROR = E INC = (PUSHED•7’•A) + (PUSHED•8’•B) + (PUSHED•9’•C) CLRTIMER = ECNT3•E CLRCNTR = (WAITDONE•F) + (LOCKED•D) UNLOCK = (PUSHED•9•C) ECEn 224

  22. Other State Encoding Techniques • You have learned the 2 extremes • Fully encoded (8 states  3 state bits) • One-hot encoded (8 states  8 state bits) • A range of options exist in between • A good choice of encoding • Can minimize IFL and OFL complexity • Algorithms have been developed for this… • Beyond the scope of this class ECEn 224

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