fall 2004ee 3563 digital systems design ee3563 chapter 7, 8, 10 reading assignments 7.1, 7.2, 7.3 ...

Fall 2004 EE 3563 Digital Systems Design

EE3563 Chapter 7, 8, 10 Reading Assignments

7.1, 7.2, 7.3 8.1, 8.2.1-8.2.3, 8.2.5 8.4.1-8.4.3 8.5.1, 8.5.2, 8.5.4 8.8 10.1, 10.2, 10.3.1-10.3.4, 10.4.1, 10.4.2


EE3563 Revisit Transfer Curve


EE 3563 Clocked Synchronous State Machines

A state machine has several components:– Next-State Logic

• Combinational logic that determines what the next state should be

– State Memory• Value of output of flip flops

– Output Logic• Flip flop output is not necessarily the final output• For example, output might be the ANDing of the flip-flop output

Clocked means that transitions only happen on the tick of a clock

Synchronous means that all transitions happen at the same time – the tick of the clock

There are 2n distinct states with n being the number of binary state variables



Mealy machine – output logic takes as input the current state as well as the machine inputs



Moore machine – output logic is solely based upon the current state

If some outputs depend on inputs and some don’t, then it is classified as a Mealy machine



Outputs may be pipelined as well, that is, the final outputs depend upon the state and inputs of the previous clock period

Pipelining can be very efficient, much like an assembly line When a machine has multiple stages, pipelining can allow

each stage to work in parallel thereby increasing efficiency



The functional behavior of a latch or flip-flop can be described with a characteristic equation

It specifies the next state as a function of inputs and current state



State machine with two positive-edge-triggered D flip-flops



Transition Table, State Table, State/Output Table



State Diagram for D-FF Mealy State Machine



State Diagram for D-FF Moore State Machine



D-FF State Machine Redrawn



Steps for analyzing a clocked synchronous circuit:– Get excitation equations

– Substitute excitation equations into flip-flop characteristic equations

– Use transition equations to construct transition table

– Get output equations

– Create transition/output table

– Name states and substitute state names for state-variable combinations to create state output table

– Draw a state diagram corresponding to the state/output table

The text goes through these steps for a different example on pages 559-560

We will go through the steps, but using the J-K flip-flop example



Get Excitation Equations



Substitute excitation equations into flip-flop characteristic equations to get transition equations

Characteristic EquationsExcitation Equations

Transition Equations



Use transition equations to construct transition table



Get output equation



Get output equation

Z = X * Q0*Q1 + Y*Q0’*Q1’



Create transition/output table

Transition Output Table



Name states and substitute state names for state-variable combinations to create state output table

State Output Table



Draw a state diagram corresponding to the state/output table

fall 2004ee 3563 digital systems design ee3563 chapter 7, 8, 10 reading assignments 7.1, 7.2, 7.3 ...

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