Feedback and Flip-Flops

Home , FLOPS

Philipp Koehn

7 September 2019

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 The Story So Far 1

• We can encode numbers

• We can do calculation

• ... but it’s all a bit static

• How about a counter? → this requires "memory"

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 2

feedback

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 A Strange Contraption 3

- +

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Let’s Turn It On 4

- +

Electricity is on → this opens the normally closed key

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Let’s Turn It On 5

- +

Electricity is off → this closes the normally closed key

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 What Do We Have? 6

• A Buzzer

• A Clock

• An Oscillator

NOT

(symbol)

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Oscillator 7

• Period of oscillator

• Frequency: cycles per second

• Unit: 1 cycle per second: 1 Hertz

• Modern computes: Billions of Hertz = Gigahertz (GHz) Heinrich Hertz 1857--1894

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 8

flip flop

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Another Contraption 9

NOR V NOR OUT

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Closing Upper Key 10

NOR V NOR OUT

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Opening Upper Key 11

NOR V NOR OUT

Same key configuration as initially But: Now OUT is on --- we remembered the key turn

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Closing Lower Key 12

NOR V NOR OUT

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Opening Lower Key 13

NOR V NOR OUT

Back to initial state

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Memory 14

• We have memory -- called Reset-Set Flip-Flop

• Truth table

UPPER LOWER OUT 0 0 OUT 0 1 0 1 0 1 1 1 Illegal

• UPPER = SET

• LOWER = RESET

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Re-Arranged 15

S NOR

NOR Q R

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Symmetric 16

S NOR Q

NOR Q R

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Truth Table 17

S R Q Q¯ 1 0 1 0 0 1 0 1 0 0 Q Q¯ 1 1 Illegal

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 18

d-type flip flop

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Vision 19

• Control bit ("clock") – on = write to memory – off = read from memory

• Data bit – data item to be written

• Output – current state of the memory

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Replace Set/Reset with Data 20

DATA NOR Q NOT

NOR Q

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Add Control Bit ("Clock") 21

DATA AND NOR Q NOT

CLOCK NOR Q AND

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 D-Type Flip-Flop 22

• Also called D-type latch

• Circuit latches on one bit of memory and keeps it around

• Truth table

Data Clock Q Q¯ 0 1 0 1 1 1 1 0 X 0 Q Q¯

• Can also build these for multiple data bits

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 23

accumulative adder

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Design Goal 24

• Adder has initially value 0

• Adding a number → value increases

• Resetting → value goes back to 0

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Ingredients 25

A7 A6 A5 A4 A3 A2 A1 A0 B7 B6 B5 B4 B3 B2 B1 B0

CO 8-BIT ADDER CI S7 S6 S5 S4 S3 S2 S1 S0

D7 D6 D5 D4 D3 D2 D1 D0

CLK 8-BIT LATCH Q7 Q6 Q5 Q4 Q3 Q2 Q1 Q0

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Ingredients 26

8 8 A B CO 8-BIT ADDER CI S 8

8 D CLK 8-BIT LATCH Q 8

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Building an Accumulative Adder 27

• Latch: current sum CLOCK CLK D 8-BIT LATCH Q • Clock on → set it to 0 8

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Building an Accumulative Adder 28

• Adder CLOCK CLK D 8-BIT LATCH Q IN • Combines 8 8

– current value A B 8-BIT ADDER – selected input CO S CI

OUT

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Building an Accumulative Adder 29

• Can we pass output CLOCK CLK D 8-BIT LATCH directly to latch? Q IN

8 8 Concerns • A B 8-BIT ADDER – select between 0 and sum CO S CI

– only stored when clock on 8

OUT

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Building an Accumulative Adder 30

0 8 8

Clear A B 2-1 SELECTOR S 8 • 2-1 selector CLOCK CLK D 8-BIT LATCH Q IN • Either uses 0 or sum 8 8

A B • Built with AND gates 8-BIT ADDER CO S CI

8 • Still have runaway feedback loop... OUT

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Building an Accumulative Adder 31

0 8 8

Clear A B • Two Latches 2-1 SELECTOR S – one to store the sum 8 CLOCK1 CLK D – one to store input to adder 8-BIT LATCH QS • Clock 1 8 CLOCK2 CLK D 8-BIT LATCH – carry out addition Q IN

– store result 8 8

A B • Clock 2 8-BIT ADDER CO S CI – transfer to set up next addition 8

OUT

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Building an Accumulative Adder 32

0 8 8

Clear A B • Combine the clocks 2-1 SELECTOR S Add 8 • Pressing the add key CLK D 8-BIT LATCH NOT – carry out addition QS – store result in upper latch 8 CLK D 8-BIT LATCH IN • Release the add key Q 8 8 – transfer to lower latch A B – set up next addition 8-BIT ADDER CO S CI

OUT

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 What Else? 33

0 8 8

Clear A B 2-1 SELECTOR S • Remember the oscillator? Add 8 CLK D NOT 8-BIT LATCH NOT QS 8

CLK D 8-BIT LATCH Q IN

8 8

A B 8-BIT ADDER CO S CI

OUT

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 What Else? 34

0 8 8

Clear A B 2-1 SELECTOR S 8

NOT CLK D 8-BIT LATCH NOT QS 8

CLK D 8-BIT LATCH Q IN

• Each cycle of oscillator: 8 8

A B keeps adding 8-BIT ADDER CO S CI

OUT

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 What Else? 35

0 8 8

Clear A B 2-1 SELECTOR S 8

NOT CLK D 8-BIT LATCH NOT QS 8

CLK D 8-BIT LATCH Q IN

• We have something interesting here 8 8

A B 8-BIT ADDER CO S CI

OUT

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 36

edge triggered flip-flop

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 D-Type Latch 37

D Q LATCH CLK Q

• When clock is on, save data

• "Level-triggered"

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 D-Type Latch 38

D Q D Q LATCH LATCH NOT CLK Q CLK Q

• "Edge-triggered": changes value, when switched from 0 to 1

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Edge Triggered D-Type Latch 39

D Q > CLK Q

Symbol

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Truth Table 40

Data Clock Q Q¯ 0 ↑ 0 1 1 ↑ 1 0 X 0 Q Q¯

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 41

ripple counter

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Oscillator and Latch 42

D Q NOT > CLK Q

Data Clock Q Q¯ 1 0 0 1 1 ↑ 1 0 0 1 1 0 0 0 1 0 0 ↑ 0 1 1 1 0 1 1 0 0 1

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Oscillator and Latch 43

D Q NOT > CLK Q

Data Clock Q Q¯ 1 0 0 1 1 ↑ 1 0 0 1 1 0 0 0 1 0 0 ↑ 0 1 1 1 0 1 1 0 0 1

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Halving of Frequency 44

Data Clock Q Q¯ 1 0 0 1 1 ↑ 1 0 0 1 1 0 0 0 1 0 0 ↑ 0 1 1 1 0 1 1 0 0 1

OUT

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Multiple Bits 45

OUT0 OUT1 OUT2 OUT3 NOT D Q D Q D Q NOT > CLK Q > CLK Q > CLK Q

OUT0

OUT1

OUT2

OUT3

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Ripple Counter 46

OUT0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

OUT1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1

OUT2 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1

OUT3 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019