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Sequential Circuits

Sequential Circuits. Design. Inputs. output logic. Outputs. next state logic. Next State. Current State. Sequential Circuits. x. A. Q. D. A. Q. C. B. Q. D. Q'. C. C lock. y. Design Example : Sequence Recognizer.

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Sequential Circuits

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  1. SequentialCircuits Design

  2. Inputs outputlogic Outputs next statelogic Next State Current State SequentialCircuits x A Q D A Q C B Q D Q' C Clock y

  3. DesignExample: SequenceRecognizer • A sequential circuit that recognizes the occurrencethe bit sequence 1101 (The sequence 1101 must be recognized each time it occurs in the input sequence.) • Thus, the sequential machine must remember that the first two one's have occurred as it receives another symbol. • Input: X(t)  {0, 1} Output: Z(t)  {0, 1} Time 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 X(t) 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 0 1 Z(t) 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1

  4. S1 S2 S3 ObtainTheStateDiagran Time 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 X(t) 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 0 1 Z(t) 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1/1 1/0 0/0 1/0 S0 1/0 0/0 0/0 0/0 A Mealy Machine

  5. ObtainState Table 1/1 • From the State Diagram, we can fill in the State Table. • Assignbinarycodesforthestates 1/0 0/0 1/0 00 01 10 11 1/0 0/0 0/0 0/0

  6. Find Flip-Flop Input and Output Equations • Selecttheflip-floptypes. (D flipflop) • Deriveflip-flopinputequations. AB X AB X

  7. X Z DrawLogicDiagram Clock

  8. One Flip-flop per State (One-Hot) Assignment 1/1 1/0 0/0 1/0 0001 0010 1000 0100 • Provides simplified analysis and design • Combinational logic may be simpler, but flip-flop cost higher 1/0 0/0 0/0 0/0

  9. 00 A/00 B/01 C/10 DesignExample: modulo 3 accumulator for 2-bit operands • It adds each input operand to the stored sum, which is initially 0. Thentakesthemodulo. • (2 + 0) modulo 3 = 2, (1+2) modulo 3 = 0 … • Stored sum: (Y1,Y0), Input: (X1,X0), Output: (Z1,Z0) Reset MealyorMoore? 01

  10. A×B A×B S0 S1 S0 S1 A + B A + B Y, Z A/Y, B/Z S2 S2 TCI Outputs Moore Outputs C/Y A×B/Y A×B S0 S1 S0 S1 C/Y (A + B)/Z (A + B) S2 S2 TCD Outputs The State Machine Diagram Model (SMD) • Input Variables A, B, COutput Variables Y, ZDefault: Y = 0, Z = 0 Transition condition (TC) Transition condition-independent (TCI) Transition condition-dependent (TCD) Transition andoutputcondition-dependent (TCOD) TCOD Outputs

  11. Example-1 Defaults: Y = 0, Z = 0 Y, Z A/Y, B/Z A×B S0 S1 A + B BC A×C A/Z A + C B×C A/Y (B + C)/Z S2 S3 B×C/Y What is thestatetableforthis SMD?

  12. Example-2 What is the SMD forthisstatediagram?

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