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 = (D 0 D 1 D 2 D 3 ) On positive edge of Clock Clear signal normally high ♦ Power-up reset

4 Register with Load Control If load signal is H ♦ D 0, D 1, D 2, D 3 reach inputs of FFs If load signal is L, Q is fed back ♦ Q 0, Q 1, Q 2, Q 3 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 Can describe inputs to FF with logic equations Same as S-R flip-flop with J analogous to S and K analogous to R Except that J = K = 1 is allowed, For J = K = 1, the flip-flop changes to the opposite state

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

9 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}

10 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)}

11 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

12 State Table Just truth table with state added At time t At time t+1

13 Two Dimensional State Table Same thing, different layout

14 Sequential Circuit Types Moore model – outputs depend on states Mealy model – outputs also depend on inputs

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

16 Mealy Model Output depends on input and state Input/Output State Table for Circuit of Figure State Table for Circuit of Figure 5-15

17 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