Flip-flops, Latches and State

Prof. Sirer

COMP 303

Koç University

Early Transistors

The first transistor, on a workbench at AT&T Bell Laboratories in 1947

Logic Gates

One can buy gates separately

ex. 74xxx series of integrated circuits

cost ~$1 per chip, mostly for packaging and testing

Cumbersome, but possible to build devices using gates put together manually

Integrated Circuits

Or one can manufacture a complete design using a custom mask

An Intel Pentium has approximately 125 million transistors

Special-Purpose Transistors

A photo-sensitive transistor can be used to detect the presence of light

Photo-sensitive material triggers the gate

RecapWe have enough tools in our arsenal to start build interesting devices

Let’s build a Scantron device

Background: A vote is recorded on a piece of paper, by punching out a hole, there are at most 7 choices we will not worry about “hanging chads” or “invalids”

For now, let’s just display the numerical identifier to the ballot supervisor

we won’t do counting yet, just decoding we can use four photo-sensitive transistors to find out which

hole is punched out

Ballot Reading

All we want to do is go from a paper with a hole in it to a number the ballot supervisor can recordBallots The super-duper

COMP303 vote decodingmachine

Demultiplexors/Encoders

N sensors in a rowWe want to distinguish which sensor of the N sensors has firedWant to represent the firing sensor number in compact form

N might be large, I want to sell this device to Italy

Only one wire is on at any time

Silly to route N wires everywhere, better to encode in log N wires

a

bo0

1

c

d

2

3

4

o1

A 3-bit (7-to-3)encoder

(4 inputs shown)

o2

Number Representations

Decimal numbers are written in base 10

3 x 101 + 7 x 100 = 37

Can just as easily use other bases

Base 2 - “Binary” Base 8 - “Octal” Base 16 – “Hexadecimal”

Base conversion via repetitive division

Divide by base,write remainder,move left with quotient

Sanity check with 37 and 10

37101 100

Binary Representation

010010126 25 24 23 22 21 20

37 = 32 + 4 + 1

64 32 16 8 4 2 1

Hexadecimal Representation

37 decimal = (25)16

Convention Base 16 is written with a leading

0x 37 = 0x25

Need extra digits! 0, 1, 2, 3, 4, 5, 6, 7,

8, 9, A, B, C, D, E, F

Binary to hexadecimal is easy Divide into groups of 4, translate

groupwise into hex digits

25161 160

Encoder Truth Table

a

b

1

c

d

2

3

4

o1

A 3-bitencoderwith 4 inputsfor simplicity

a b c d o2 o1 o0

0 0 0 0 0 0 0

1 0 0 0 0 0 1

0 1 0 0 0 1 0

0 0 1 0 0 1 1

0 0 0 1 1 0 0

o0

o1

o2

o2 = abcd

o1 = abcd + abcd

o0 = abcd + abcd

Ballot Reading

Ok, we builtfirst half of the machine

Need to display the result

Ballots The super-duperCOMP303 vote decoding

machine

7-Segment LED Decoder

4 inputs encoded in binary

8 outputs, each driving an independent, rectangular LED

Can display numbersJust a simple logic circuit

Write the truth table

7-Segment LED Decoder

4 inputs encoded in binary

8 outputs, each driving an independent, rectangular LED

Can display numbers

01

00

7-Segment LED Decoder

4 inputs encoded in binary

8 outputs, each driving an independent, rectangular LED

Can display numbers

01

10

7-Segment Decoder Truth Table

i3 i2 i1 i0 o0 o1 o2 o3 o4 o5 o6

0 0 0 0 1 1 1 0 1 1 1

0 0 0 1 1 0 0 0 0 0 1

0 0 1 0 1 1 0 1 1 1 0

0 0 1 1 1 1 0 1 0 1 1

0 1 0 0 1 0 1 1 0 0 1

0 1 0 1 0 1 1 1 0 1 1

0 1 1 0 0 0 1 1 1 1 1

0 1 1 1 1 1 0 0 0 0 0

1 0 0 0 1 1 1 1 1 1 1

1 0 0 1 1 1 1 1 0 1 1

o0

o1

o2

o3

o4

o5

o6

Exercise: find the error(s) in this truth table

7-Segment Decoder Truth Table

i3 i2 i1 i0 o0 o1 o2 o3 o4 o5 o6

0 0 0 0 1 1 1 0 1 1 1

0 0 0 1 1 0 0 0 0 0 1

0 0 1 0 1 1 0 1 1 1 0

0 0 1 1 1 1 0 1 0 1 1

0 1 0 0 1 0 1 1 0 0 1

0 1 0 1 0 1 1 1 0 1 1

0 1 1 0 0 0 1 1 1 1 1

0 1 1 1 1 1 0 0 0 0 1

1 0 0 0 1 1 1 1 1 1 1

1 0 0 1 1 1 1 1 0 1 1

o0

o1

o2

o3

o4

o5

o6

Ballot Reading

Done!

Off to the patent office!

Ballots The super-duperCOMP303 vote decoding

machine

Keyboard

Let’s build a keyboard Lots of mechanical

switches Need to convert to a

compact form (binary)

We’ll use a special mechanical switch that, when pressed, connects two wires simultaneously

Keyboard

When a key is pressed, a 7-bit key identifier is computed

+

3-bitencoder(4 to 3)

4-bitencoder(16 to 4)

not all 16 wires are shown

Stateful Components

Everything we did until now is combinatorial logic Output is computed when inputs are present The system has no internal state Nothing computed in the present can depend

on what happened in the past!

Need a way to record dataNeed a way to build stateful circuitsNeed a state-holding device

Bistable Devices

In stable state, A = B

How do we change the state?

A B

A B

1

A B

10 0

A Simple Device

SR Latch

Set-Reset (S-R) LatchQ: Stored value and its complement

S=1 and R=1 ?

S

RQ

Q

S R Q Q

0 0 Q Q

0 1 0 1

1 0 1 0

1 1 ? ?

D Latch

Data Latch Easier to use than an SR latch No possibility of entering an undefined state

When D changes, Q changes … immediately

Need to control when the output changes

S

R

Q

QD

Clocks

Clocks help with modifying the contents of state-holding elements

A free running signal Generated by an oscillating crystal

Clock signal has a fixed cycle time (aka cycle period)

Clock frequency = 1/cycle time

clockperiod

clockhigh

clocklow

1

0

fallingedge

risingedge

Edge-triggering

Can design circuits to change on the rising or falling edge

Trigger on rising edge = positive edge-triggered

Trigger on falling edge = negative edge-triggered

Inputs must be stable just before the triggering edgeinput

clock

First Attempt

How does the output behave?

S

R

D

clk

D

clk

Q

Q

Q

Q

D Q

Q

First Attempt

How does the output behave?

S

R

D

clk

Q

Q

clk

D

Q

First Attempt

How does the output behave?

Changes in D that occur when the clock is low are deferred until clock high

Changes when clock is high are registered immediately

S

R

D

clk

D

clk

Q

Q

Q

Q

D Q

Q

Master-Slave Flip-FlopOutputs change only on falling edgesData is captured on rising edges1/2 cycle delay but works out

perfectly – data for the next stage is ready 1/2 cycle ahead of time

D Q

Q

D Q

Q

clk

D

X

Q

X

Keyboard

When a key is pressed, a 7-bit key identifier is computedLet’s store this keycode The computer

may not be ready to read it right away

+

3-bitencoder(4 to 3)

4-bitencoder(16 to 4)

not all 16 wires are shown

Registers

A register is simply a set of master-slave flip-flops in parallel with a shared clock

D Q D Q

D Q D Q

D Q D Q

D Q D Q

clk

D0

D3

D1

D2

4 4

4-bitreg

One-Shot

A simple device that, when triggered, produces a pulse of the specified width

in one shotX ms

out

in

out

X ms

Keyboard with Last Key Display

+

3-bitencoder(4 to 3)

4-bitencoder(16 to 4)

not all 16 wires are shown

4-bitreg

7seg

deco

7seg

deco

4-bitreg

one-shot1ms

Summary

We can now build interesting devices with sensors Using combinatorial logic

We can also store data values In state-holding elements Coupled with clocks