Analysis and Synthesis of Synchronous Sequential Circuits

• A “synchronizing” pulse/edge signal (clock) controls the operation of the memory portion of the circuit

• When noclock – thecircuit is asynchronous:

Analysis and Synthesis of Synchronous Sequential Circuits

• The “state” of a synchronous sequential circuit:– All the FF/memory element outputs– Can change only upon clock transition (pulse/edge)

• Two models for synchronous sequential circuits:– Mealy model

• Outputs are a function of state and inputs

– Moore model• Outputs are a function of state only

Mealy model

• Next state (Y1,…,Yr) achieved on clock transition

Mealy model

• Input (x1,…,xn), output (z1,…,zm), present state (y1,…,yr) and next state (Y1,…,Yr) are

where gi and hi are Boolean functions, or in vector form

Moore model

Combinational logic

Combinational logic

Memory

x1

xn

Y1

Yr

y1

yr

z1

zm

clock

Mealy machine example

• State diagram and state table

• Assumes transitions

Problem?

Moore machine example

• State diagram and state table

• Output is f(state) only• Inputs – no effect

Mealy vs. Moore

• Representations can be transformed into each other

• Advantages and disadvantages

Mealy Moore

- glitches + no glitches

- problem sampling

+ easier to design

+ lesser total # states

Analysis precedes synthesis

• Analysis of logic diagrams of sequential circuits– Inputs, state variables, outputs, logic equations ?– Mealy or Moore type?

Analysis

– Input sequence: x = 01101000

yxyxyxY

xyz

Analysis

• Deriving state diagram and state table– Given circuit diagram Boolean equations

• Notation: yk represents y(k t)• k = integer; t = clock period

• May assign numbers to states: 0 state A; 1 state B

Analysis

• Deriving state table from K-maps

Map for Yk=yk+1 Map for zk

Analysis example

• Synchronous sequential circuit with flip-flops– Negative edge-

triggered– Inputs?– States?– Outputs?– Logic equations?

Analysis example

• Timing diagram

Analysis example

• State table and K-maps

Analysis example

• Combining the K-maps into state table