Week 14, Lect.1/2

Quiz on Ch.7

1] Explain the operation of this T Flip-Flop with Enable:

How does the circuit operate when EN= 1? (Words and diagram)

When EN = 0?

2] Explain in a short paragraph the meaning of Setup time and Hold time.

Ch.8 Designing Synchronous Sequential Circuits

Motivation: In Ch.7 we have seen several times the idea of mixing

sequential and combinational circuits in order to obtain larger

circuits with desired behavior,

e.g. binary counter:

e.g. the control unit for register-swapping:

… but all these are “just so” contraptions! (similar to the MUX for

combinational circuits)

Is there a general method to design our own sequential circuits from

scratch? (similar to the truth table + SOP method for combinational)

Q: What is the state of a sequential circuit?

A: The combination of the states (Q values) of all flip-flops.

Finite state machine (FSM)

→ with N flip-flops, how many states are possible?

Synchronous FSM (SFSM?)

the CLKs of all flip-flops are connected in parallel to a “master

CLK” signal

structure of an (S)FSM:

Moore → All paths between I and O go through a Flip-Flop

Mealy → There is at least one path between I and O that does

not go through a FF

Pattern recognition: Moore or Mealy? (Not in text!)

End – Moore or Mealy

Name the parts of a Moore/Mealy machine (not in text!):

As with combinational circuits, problems involving FSMs can be of

two types:

Analysis → Given the circuit, figure out the sequence of states

Design (a.k.a. synthesis) → Given the sequence of states,

design a machine that implements it

Asynchronous

I/O path

8.1 Basic design steps

Problem: Design the following sequence detector:

One input w

One output z

All changes occur at positive edge of CLK

z = 1 if during the two immediately preceding CLK cycles the

input w was 1

z = 0 otherwise

Design algorithm

Draw the symbol (black-box) for the circuit, w/inputs and outputs

Decide if a sequential circuit is needed

To answer this, we may want to try out some sequences of inputs,

like this:

Conclusion: The output does not depend on input alone!

Draw the state diagram

Extra-credit: Can you tell just by looking at the diagram if it’s

Moore or Mealy? (Must explain for credit!)

Draw the next state table

Perform state assignment …

Draw the state-assigned table

Sketch the outline of a Moore/Mealy machine, with the required

number of flip-flops

Choose type of Flip-Flops → We’ll only use D (JK may lead to

simpler next-state logic, read Section 8.7 FYI)

From the state-assigned table, extract separate truth tables for the D

input of each FF.

Design the next-state logic and output logic (all combinational!) Here we can use all the design and optimization techniques we learned for

combinational circuits: canonical SOP, K-maps, functional

decomposition, multiple-output optimization

Draw final circuit diagram

The text includes a timing diagram after this, but it’s really an

analysis tool …

To do in notebook for next time:

READ and take notes → Section 8.1 (pp.487-497)

Understand Example 8.1/494

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Quiz:

What does FSM stand for?

Moore or Mealy?

Explain and mark the relevant path(s) on the diagram (handout)

Another application of flip-flops: Remember the CPLD blocks …

Application of FSM

Algorithm for swapping contents of R1 and R2, using R3:

CLK1 Load R2 into R3 signals …

CLK2 Load R1 into R2 signals …

CLK3 Load R3 into R1 signals …

Turn on additional output Done

R3

R3in R3out

n

Moore or Mealy?

8.2 State assignment

By assigning the binary codes for the states in a clever way,

we can minimize the hardware required!

To do in notebook for next time: Example 8.2

The simplest combinational logic: “one-hot”

Advantage: Next-state combinational logic is simpler.

Disadvantage: # of Flip-Flops is equal to # of states (instead

of logarithmic)

To do in notebook for next time: Example 8.3

8.3 Designing Mealy machines

Problem: “11 detector”, but we want the output to turn to 1 in the same cycle

in which the second one is detected!

How to turn a Mealy into a Moore:

For more practice:

Implement a two-input Mealy machine that produces a 1 at its single

output when the values of the two inputs differ at the time of the

previous clock pulse. Show your state -diagram or ASM chart.

Describe what each of your states is supposed to represent.

8.4 Designing FSMs with VHDL

SKIP the rest of Section 8.4

8.5 Design example: SERIAL ADDER

All the combinational adders we studied in Ch.5 perform the

additions of the bits (more or less) in parallel

Advantage: Speed!

Disadvantage: Lots of hardware!

O(n) for ripple-carry, a little higher if we want lookahead

If speed is not an issue, serial adders can save a lot of

hardware!

O(log n)

Let’s design the Adder FSM!

Do you notice any parity pattern in s?

Moore or Mealy?

SKIP the rest of Section 8.5

This concludes the material required for the final

Tuesday class → REVIEW!

See you this afternoon for our last lab!