Flip-flops, Latches and State

1
Flip-flops, Latches and State

• Prof. Sirer
• CS 316
• Cornell University

2
Early Transistors

• The first transistor, on a workbench at ATT Bell
  Laboratories in 1947

3
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

4
Integrated Circuits

• Or one can manufacture a complete design using a
  custom mask
• An Intel Pentium has approximately 125 million
  transistors

5
Special-Purpose Transistors

• A photo-sensitive transistor can be used to
  detect the presence of light
• Photo-sensitive material triggers the gate

6
Recap

• We have enough tools in our arsenal to start
  build interesting devices
• Lets build a Scantron device
• Elections are coming up!
• Background
• A vote is recorded on a piece of paper,
• by punching out a whole,
• there are at most 7 choices
• we will not worry about hanging chads or
  invalids
• For now, lets just display the numerical
  identifier to the ballot supervisor
• we wont do counting yet, just decoding
• we can use four photo-sensitive transistors to
  find out which hole is punched out

7
Ballot Reading

• All we want to do is go from a paper with a hole
  in it to a number the ballot supervisor can record

Ballots
The super-duper 316 vote decoding machine
8
Demultiplexors/Encoders
a
1

• N sensors in a row
• We want to distinguish which sensor of the N
  sensors has fired
• Want 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

o0
b
2
o1
c
3
o2
d
4
A 3-bit (7-to-3) encoder (4 inputs shown)
9
Number Representations
37

• Decimal numbers are written in base 10
• 3 x 101 7 x 100 37
• 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

101 100
10
Binary Representation

• 37 32 4 1

0100101
26 25 24 23 22 21 20
64 32 16 8 4 2 1
11
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

25
161 160
12
Encoder Truth Table
a
1
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
b
2
o1
o1
c
3
o2
d
4

• o2 abcd
• o1 abcd abcd
• o0 abcd abcd

A 3-bit encoder with 4 inputsfor simplicity
13
Ballot Reading

• Ok, we builtfirst half of the machine
• Need to display the result

Ballots
The super-duper 316 vote decoding machine
14
7-Segment LED Decoder

• 4 inputs encoded in binary
• 8 outputs, each driving an independent,
  rectangular LED
• Can display numbers

• Just a simple logic circuit
• Write the truth table

15
7-Segment LED Decoder

• 4 inputs encoded in binary
• 8 outputs, each driving an independent,
  rectangular LED
• Can display numbers

1
0
0
0
16
7-Segment LED Decoder

• 4 inputs encoded in binary
• 8 outputs, each driving an independent,
  rectangular LED
• Can display numbers

1
0
1
0
17
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
o1
o0
o2
o3
o4
o6
o5
Exercise find the error(s) in this truth table
18
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
o1
o0
o2
o3
o4
o6
o5
19
Ballot Reading

• Done!
• Off to the patent office!

Ballots
The super-duper 316 vote decoding machine
20
Keyboard

• Lets build a keyboard
• Lots of mechanical switches
• Need to convert to a compact form (binary)
• Well use a special mechanical switch that, when
  pressed, connects two wires simultaneously

21
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
22
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 data
• Need a way to build stateful circuits
• Need a state-holding device

23
Bistable Devices
A
B
A Simple Device

• In stable state, A B
• How do we change the state?

1
0
0
1
A
B
A
B
24
SR Latch
Q
R
S
Q

• Set-Reset (S-R) Latch
• Q Stored value and its complement
• S1 and R1 ?

S R Q Q
0 0 Q Q
0 1 0 1
1 0 1 0
1 1 ? ?
25
D Latch
Q
R
D
S
Q

• 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

26
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

risingedge
fallingedge
1
0
clock period
clock high
clock low
27
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
  edge

input
clock
28
First Attempt
D
S

• How does the output behave?

Q
R
Q
clk
D
Q
D
Q
clk
Q
Q
29
First Attempt
D
S

• How does the output behave?

Q
R
Q
clk
clk
D
Q
30
First Attempt
D
S

• 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

Q
R
Q
clk
D
Q
D
Q
clk
Q
Q
31
Master-Slave Flip-Flop

• Outputs change only on falling edges
• Data is captured on rising edges
• 1 cycle delay
• but works out perfectly data for the next stage
  is ready 1 cycle ahead of time

D
Q
D
Q
X
Q
Q
clk
D
X
Q
32
Keyboard

• When a key is pressed, a 7-bit key identifier is
  computed
• Lets 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
33
Registers
D0
D
Q
D
Q

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

D1
D
Q
D
Q
D2
D
Q
D
Q
4-bit reg
4
4
D3
D
Q
D
Q
clk
34
Keyboard with Last Key Display

4-bit reg
7 seg deco
3-bitencoder (4 to 3)
4-bitencoder (16 to 4) not all 16 wires are shown
7 seg deco
4-bit reg
35
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