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Registers; State Machines Analysis

This section delves into the fundamentals of registers and state machines, essential concepts in digital circuit design. A register is defined as a set of flip-flops that can hold data and control state transitions. The analysis begins with simple registers, explaining their operation on the positive clock edge with clear signals. We explore synchronous sequential circuits using state tables and diagrams, illustrating how to determine next states and outputs based on current states and inputs. The Moore and Mealy models are discussed, highlighting their differences and applications in circuit design.

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Registers; State Machines Analysis

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  1. Registers; State Machines Analysis Section 7-1 Section 5-4

  2. Definition • Register – a set of flip-flops • May include extensive logic to control state transition • register also refers to fast memory for storing data in a computer

  3. Simple Register • Store D = (D0 D1 D2 D3) • On positive edge of Clock • Clear signal normally high • Power-up reset

  4. Register with Load Control • If load signal is H • D0 , D1 , D2 , D3 reach inputs of FFs • If load signal is L, Q is fed back • Q0 , Q1 , Q2 , Q3 reach inputs of FFs • FFs Keep same value

  5. State Machines: Analysis and Design • How to design machines that go through a sequence of events • Basically close this loop

  6. Analysis of Sequential Circuits • Earlier we learned how to analyze combinational circuits • Now extend to synchronous sequential • Include time • We’ll use state tables and state diagrams

  7. Input Equations: D FF Example Describe inputs to FF with logic equations

  8. Determining Next State and Output Current state= {A(t), B(t)} = values stored in FFs during clock t Next state= {A(t+1), B(t+1) = values stored in FFs during clock t+1}

  9. Determining Next State and Output The current state {A(t), B(t)} & input X are used to determine next state {A(t+1), B(t+1)}

  10. Determining Next State and Output (cont.) Current state & input X are used to determine output, Y • Synchronous circuit • State transitions are at positive edge of clock

  11. At time t+1 At time t State Table • Just truth table with state added

  12. Two Dimensional State Table • Same thing, different layout

  13. Sequential Circuit Types • Moore model – outputs depend on states • Mealy model – outputs also depend on inputs

  14. Inputs State/Output State Diagram • Alternative representation for state table • Moore: outputs depend only on states

  15. Input/Output --------------------------------------------- State Table for Circuit of Figure 5-15 Mealy Model • Output depends on input and state State Table for Circuit of Figure 6-17

  16. State Table vs. Diagram • Same information • Table is perhaps easier to fill in from description • Diagram is easier for understanding and writing code • You can label states with English description

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