Analysis and Synthesis of
Synchronous Sequential Circuits
• A “synchronizing” pulse/edge signal (clock)
controls the operation of the memory portion of
the circuit
• When no
clock – the
circuit 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
x1
xn
y1
Combinational logic
Y1
Yr
Memory
yr
clock
Combinational logic
z1
zm
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
z  xy
Y  xy  xy  x  y
– Input sequence: x = 01101000
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 flipflops
– Negative edgetriggered
– 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