Overview of course content Specification of digital functions and - - PowerPoint PPT Presentation

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Overview of course content Specification of digital functions and - - PowerPoint PPT Presentation

May 04, 2023 107 likes •581 views

Overview of course content Specification of digital functions and system Digital building blocks Combinatorial systems Digital Arithmetic Synchronous systems and state

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SLIDE 1

Overview of course content

William Sandqvist william@kth.se

  • Specification of digital functions and system
  • Digital building blocks
  • Combinatorial systems
  • Digital Arithmetic
  • Synchronous systems and state machines
  • Asynchronous systems and state machines
  • A little larger digital systems - the CPU and

computers VHDL is not significantly included - because it will need a complete course for itself.

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SLIDE 2

Digital Design IE1204

William Sandqvist william@kth.se

Digital Design Everywhere!

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SLIDE 3

William Sandqvist william@kth.se

40-100 microprocessors in a car!

  • Ignition system
  • Emission control

system

  • Anti-lock brakes
  • Dashboard display
  • Entertainment system
  • Navigation system
  • . . .
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SLIDE 4

The development of electronics

William Sandqvist william@kth.se

Intel 4004 (1971) 108 KHz 2,300 transistors Intel Xeon 5400 (2008) 3.0 GHz 820 millions of transistors If there had been a corresponding development of the car speed, one would be able to drive from San Francisco to New York in about 13 seconds (Intel).

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SLIDE 5

Why is digital technology so successful?

William Sandqvist william@kth.se

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SLIDE 6

Simplicity, imunity of electromagnetical disturbances.

William Sandqvist william@kth.se

  • Simple mathematical model

– with only 1's and 0's as values – Boolean algebra

  • Imunity of electromagnetical disturbances,

effective implementation of the mathematical model

– Transistors – Integrated circuits – Advances in semiconductor technology

  • Efficient design methods and tools
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SLIDE 7

Analog or Digital signals?

William Sandqvist william@kth.se

000 001 010 001 010 011 100 100 011 011

101 100 011 010 001

time 5 4 3 2 1

An analog signal can assume continuous values, while a digital signal may assume only discrete values (here, 0 ... 5)

value Analog continuous signal Digital signal with discrete values

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SLIDE 8

Digital should be worse?

William Sandqvist william@kth.se

0001 0011 0101 0011 0101 0111 1001 1001 0111 0111

1011 1001 0111 0101 0011

Analog signal Digital signal (3 bits)

  • Digital signal (4 bits),
  • double sampling frequency

But if you have enough bits and sufficiently high sampling rate, the digital signal mimics the analog signal

value time

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SLIDE 9

Digital technology is very insensitive to interference

William Sandqvist william@kth.se Logic value 1 Undefined Logic value 0 Voltage V

DD

V

1,min

V

0,max

V

SS (Gnd)

  • It is not only one voltage value

which is translated as ”1” or ”0”, it’s a wider voltage ranges.

  • A disturbance of some mV can

affect the value of an analog signal a lot, but it will not move the value out of the digital range.

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SLIDE 10

Imunity of electromagnetical disturbances

William Sandqvist william@kth.se

Great affection Unaffected

  • Digital data processing can be done insensitive of

electromagnetic disturbances! Analog: Digital:

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SLIDE 11

Digital Signal Processing

ADC Digital Signal processing

Microphone Antenna Analog signal Digital signals

01101010100 1010101 10 101010

Carrier frequency Modulated signal

DAC

Analog-Digital Converter Digital-Analog Converter

11 IE1204 Digital Design

When possible all signal processing is done digitally today

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SLIDE 12

Catching the data is still critical!

William Sandqvist william@kth.se

Although most of the signal processing is now done digitally and thus safe from interference, it is still critical to "catch" the data in a good way – the analog / digital conversion! Any disturbancies that accompany the data into the digital system we then will have to live with! 100111011101111011110

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SLIDE 13

Mathematical model - Boolean algebra: axioms

William Sandqvist william@kth.se

  • In Boolean algebra, there is only one (true) and 0 (false) as

values

  • The following operations are defined: AND (), OR (+),

NOT (x)

  • The following axiom defines the Boolean algebra
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SLIDE 14

Booleska Algebra: rules

William Sandqvist william@kth.se

Rules can be derived from axioms

– many of the rules are consistent with our usual algebra! – comfortable that we can continue to use rules as has been done in primary school! – but beware! Some rules are new and different!

  • More soon in the course ...
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SLIDE 15

The technical background

William Sandqvist william@kth.se

When telephone exchanges were automated, Boolean algebra was used as a tool to calculate how the networks could be simplified. The switches is drawn in their unaffected state.

Making contact Breaking contact, ”not” + for parallell connection the ”or”-function

⋅ ⋅ ⋅ ⋅ for serial connection,

the ”and” -function

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SLIDE 16

Gates instead of switches

William Sandqvist william@kth.se

+ ”or”-gate

⋅ ⋅ ⋅ ⋅ ”and”-gate

”not” inverter

With these three basic gate types: OR AND NOT can all logical functions be performed. The switches were eventually replaced by "gates" made of electronic components

  • More soon in the course ...
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SLIDE 17

Only one single gate type!

William Sandqvist william@kth.se

Actually it will Suffice with one single gate type, NAND, for making every other!

Extreme simplification,

  • ne single gate type is

enough for everything!

  • More soon in the course ...
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SLIDE 18

CMOS NAND - gate

William Sandqvist william@kth.se

An effective implementation of CMOS NAND gate requires only four transistors ... CMOS gates consume only effect when changing state. Good thing, otherwise today's computer chips would be even hotter. A N-MOS transistor.

  • More soon in the course ...
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SLIDE 19

Memoryfunction?

William Sandqvist william@kth.se

Traffic lights and elevators must "remember" your button presses. This is done by "flip- flops" or "latches" - which you can also make with NAND gates.

  • More soon in the course ...
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SLIDE 20

William Sandqvist william@kth.se

See-of-Gates

Because only one single type of gates is needed, you can do anything with a "sea of gates" completed with printed wires designed for its own specific function.

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SLIDE 21

William Sandqvist william@kth.se

See-of-Gates

Because only one single type of gates is needed, you can do anything with a "sea of gates" completed with printed wires designed for its own specific function.

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SLIDE 22

William Sandqvist william@kth.se

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SLIDE 23

How to design with a billion gates?

William Sandqvist william@kth.se

A modern processor can contain a billion gates - you can not draw such a circuit diagram by hand ... We need other methods to describe such a system!

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SLIDE 24

CAD-tools

  • A CAD tool is a program that helps the engineer

to design (eg, an integrated circuit)

  • CAD tools can be fully automated or interactive
  • CAD tools are based on algorithms that define

the order of a sequence of methods to be applied

William Sandqvist william@kth.se

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SLIDE 25

Hardware description languages

William Sandqvist william@kth.se

Entity Architecture Inpursignals Outputsignals

The Design is described with an entity (black box) and an architecture (the content of the box)

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SLIDE 26

Design-tools

William Sandqvist william@kth.se

VHDL-code

Equations

Implemen- tation

Step 1: VHDL-Description of the desired hardware is translated into Boolean equations Step 2: Boolean equations is translated to the available hardware

In the course You will try out the design tool Quartus II

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SLIDE 27

Example of VHDL-code

William Sandqvist william@kth.se

LIBRARY ieee ; USE ieee.std_logic_1164.all ; ENTITY mux4to1 IS PORT( w0, w1, w2, w3 : IN STD_LOGIC ; s : IN STD_LOGIC_VECTOR(1 DOWNTO 0) ; f : OUT STD_LOGIC ) ; END mux4to1 ; ARCHITECTURE Behavior OF mux4to1 IS BEGIN WITH s SELECT f <= w0 WHEN "00", w1 WHEN "01", w2 WHEN "10", w3 WHEN OTHERS ; END Behavior ;

VHDL is a very complex language - this course can not accommodate so much of this.

Advanced level courses are available!

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SLIDE 28

Boolean equation

William Sandqvist william@kth.se

f = s

1⋅ s0⋅ w0 + s 1⋅ s0⋅ w1 + s 1⋅ s0⋅ w2 + s 1⋅ s0⋅ w3

  • More soon in the course ...
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SLIDE 29

A gate circuit that implements the function

William Sandqvist william@kth.se

The textbook uses American symbols: AND OR NOT

  • More soon in the course ...
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SLIDE 30

William Sandqvist william@kth.se

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SLIDE 31

Technology Advances

William Sandqvist william@kth.se

The trend is furious fast ...

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SLIDE 32

Digital hardware in a computer

William Sandqvist william@kth.se

System Modules Gates and flip-flops Transistors

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SLIDE 33

The Designprocess

William Sandqvist william@kth.se

In the course we are simulating a design with ModelSim

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SLIDE 34

Binary numbers

William Sandqvist william@kth.se

Digital technology uses only two numerical symbols: 0 and 1

– Easy to implement - each value corresponds to a voltage level, e.g.

0 Volt corresponds to 0 5 Volt corresponds to 1

How can ordinary numbers be represented?

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SLIDE 35

Decimal number system

William Sandqvist william@kth.se

In the decimal number system we have 10 different numeric symbols: 0-9 A decimal number is represented with a sequence of numeric symbols

– The position in the sequence gives the digit its weight and is multiplied by a power of 10 (the base of the decimal system is 10)

1 2 10

10 3 10 5 10 6 ) 653 ( ⋅ + ⋅ + ⋅ =

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SLIDE 36

Decimal number system

William Sandqvist william@kth.se

1 1 2 2 1 1 10

10 10 10 10 ⋅ + ⋅ + ⋅ + ⋅ =

− − − −

x x x x N

m m m m

  • +

⋅ + ⋅ + ⋅ + ⋅ + ⋅ + ⋅ =

− − − − − − − − 2 2 1 1 1 1 2 2 1 1 10

10 10 10 10 10 10 x x x x x x N

m m m m 2 1 10

10 3 10 5 10 6 ) 53 . 6 (

− −

⋅ + ⋅ + ⋅ =

1 2 10

10 3 10 5 10 6 ) 653 ( ⋅ + ⋅ + ⋅ =

Representation of an integer Representation of a ”decimal point number”

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SLIDE 37

Binary number system

William Sandqvist william@kth.se

The binary system works the same way as the decimal system, but using base 2 instead of 10!

  • +

⋅ + ⋅ + ⋅ + ⋅ + ⋅ + ⋅ =

− − − − − − − − 2 2 1 1 1 1 2 2 1 1 2

2 2 2 2 2 2 x x x x x x N

m m m m 10 1 2 2

) 6 ( 2 2 1 2 1 ) 110 ( = ⋅ + ⋅ + ⋅ =

10 2 1 1 2

) 25 . 3 ( 2 1 2 2 1 2 1 ) 01 . 11 ( = ⋅ + ⋅ + ⋅ + ⋅ =

− −

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SLIDE 38

Octal number system

William Sandqvist william@kth.se

In the octal number system the base is 8 and therefore numerical symbols 0-7 are used

  • +

⋅ + ⋅ + ⋅ + ⋅ + ⋅ + ⋅ =

− − − − − − − − 2 2 1 1 1 1 2 2 1 1 8

8 8 8 8 8 8 x x x x x x N

m m m m 10 1 1 8

) 375 . 53 ( 8 3 8 5 8 6 ) 3 . 65 ( = ⋅ + ⋅ + ⋅ =

−

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SLIDE 39

Hexadecimal number system

William Sandqvist william@kth.se

In the hexadecimal number system the base is 16, and thus the numeric symbols 0 to 9 and A to F are used

  • +

⋅ + ⋅ + ⋅ + ⋅ + ⋅ + ⋅ =

− − − − − − − − 2 2 1 1 1 1 2 2 1 1 16

16 16 16 16 16 16 x x x x x x N

m m m m 10 1 1 16

) 5 . 174 ( 16 8 16 14 16 10 ) AE.8 ( = ⋅ + ⋅ + ⋅ =

−

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SLIDE 40

Number system with base b

William Sandqvist william@kth.se

A general formulation can be obtained for the base b

  • +

⋅ + ⋅ + ⋅ + ⋅ + ⋅ + ⋅ =

− − − − − − − − 2 2 1 1 1 1 2 2 1 1

b x b x b x b x b x b x N

m m m m b

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SLIDE 41

The integers for the different number systems

William Sandqvist william@kth.se

Base 2 Base 8

Base 10 Base 16

1 1 1 1 10 2 2 2 11 3 3 3 100 4 4 4 101 5 5 5 110 6 6 6 111 7 7 7 Base 2 Base 8

Base 10 Bas 16

1000 10 8 8 1001 11 9 9 1010 12 10 A 1011 13 11 B 1100 14 12 C 1101 15 13 D 1110 16 14 E 1111 17 15 F 10000 20 16 10

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SLIDE 42

Quickie Question

William Sandqvist william@kth.se

Discuss your answer along with your bench neighbors! What hexadecimal number corresponds to the binary number 00010111?

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SLIDE 43

Quickie Question

William Sandqvist william@kth.se

What hexadecimal number corresponds to the binary number 00010111?

1 7

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SLIDE 44

Conversion between decimal and binary numbers

William Sandqvist william@kth.se

  • Conversion from binary to decimal is trivial
  • The conversion from decimal to binary is done by repeatedly

dividing by 2

– The rest gives the numerical value – Digits are calculated in reverse order - Least Significant Bit (LSB) comes first

(MSB) 1 1 Rest 2 1 1 1 Rest 1 2 3 Rest 3 2 6 1 1 Rest 6 2 13 Rest 3 1 2 26 (LSB) 1 1 Rest 26 2 53

5 4 3 2 1

=

  • =

÷ =

  • =

÷ =

  • =

÷ =

  • =

÷ =

  • =

÷ =

  • =

÷ x x x x x x

5310 = 1101012

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SLIDE 45

Summary

William Sandqvist william@kth.se

  • There are various number systems
  • Digital technology uses the binary number

system

  • You can convert numbers between different

number systems

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SLIDE 46

William Sandqvist william@kth.se