ENG2410Digital Design

“Introduction to Digital Systems: Part 1”

S. AreibiSchool of EngineeringUniversity of Guelph

Topics

Computing Devices and VLSI Design Signals (Digital vs. Analog) Digital Systems and Computers Number systems [binary, octal, hex] Base Conversion Arithmetic Operations Decimal Codes [BCD] Alphanumeric Codes (ASCII)

Resources

Chapter #1, Mano Sections 1.1 Digital Computers 1.2 Number Systems 1.3 Arithmetic Operations 1.4 Decimal Codes 1.5 Alphanumeric Codes

Digital Systems

5

PDA

Body

Entertainment

Household

Communication

Home Networking

Car

Medicine

PC

Super Computer

Computing Devices Everywhere!

Game console

What is the main enabler to such digital systems?

Digital Circuits (Processors) found in all computing devices

Embedded Systems

6

The Transistor Revolution

First transistorBell Labs, 1948

Integrated Circuits1960’s

• Intel 4004 processor • Designed in 1971• Almost 3000 transistors• Speed:1 MHz operation

Every Processor consists of a Control Unit and a Data Path

7

Processor: Digital System

Inputs: Keyboard, mouse, modem, microphone

Outputs: CRT, LCD, modem, speakers

Controlunit DatapathCPU

Data/Instructions/codeAll in 01010010010

clock

Basic Gates

Memory

Input/Output

Transistors

9

MOSFET: Metal OxideSemiconductor

Field Effect Transistor

A voltage controlled device Handles less current than a BJT (Slower) Dissipates less powerAchieves higher density on an IC Has full swing voltage 0 5V

10

Transistor as a Switch

VGS ≥ VTRon

S D

A Switch!

|VGS|

An MOS Transistor

G

S D

If VGS is > VT the Transistor is OnElse If VGS is < VT the Transistor is Off

11

nMOS Transistor

Ids

Vgs

control gate

source drain

(a) Standard MOS transistor

Siliconsubstrate

Silicondioxide

Sourceterminal

Control gateterminal

Drainterminal

|VGS|

An nMOS Transistor

Vth

Gate

DrainSource

VLSI Design Cycle

n+n+S

GD

+

DEVICE

CIRCUIT

GATE

MODULE

SYSTEMSpecification

Functional design

Circuit design

Physical design

Test/Fabrication

Logic design

The VLSI Design Cycle

13

© K

LMH

Lien

ig

14

1.3 VLSI Design Styles Contact

Vdd

GND

OUTIN2

IN1OUT

IN2

IN1

OUTIN1

Vdd

GND

IN2

Power (Vdd)-Rail

Ground (GND)-Rail

Diffusion layer

p-typetransistor

n-typetransistor

Metal layer

Poly layer

A Digital Systems

Circuit Level Physical Level

Signals

16

SignalsAn information variable represented by a

physical quantity (speech, Temp, humidity, noise, …)

17

Signals

Signals can be analog or digital:

1. Analog signals can have an infinite number of values in a range;

2. Digital signals can have only a limited number of values.

18

Analog Signals

Analog

Time

Continuous in value & time

Continuous in Value

Continuous in Time

19

Digital Signals

For digital systems, the variable takes on discrete values (i.e., not continuous)

Time

Digital Discrete in value

Either 0 or 5 volts

20

Asynchronous

Synchronous

Discrete in value &

continuous in time

Discrete in value & time

Digital

Digital (Binary) values are represented by: digits 0 and 1 False (F) and True (T) +5 Volt and 0 Volt ……

Time

Digital: Sync vs. Async

A global clock governs the transitions of the system

21

What are other physical quantities representing 0 and 1?

Binary Values: Other Physical Quantities

CPU: Voltage Hard Drive: Magnetic Field Direction

CD: Surface Pits/LightDynamic Ram: Electric Charge

+5 volt or 0 volt MF to the right or left

Electric Charge stored in a capacitor

A bump etched is a 0, no bump is a 1

Number Representation

23

Number Systems – Representation

A number with radix r is represented by a string of digits:An - 1An - 2 … A1A0 . A- 1 A- 2 … A- m + 1 A- m

in which 0 ≤ Ai < r and “.” is the radix point. The string of digits represents the power series:

( ) ( )(Number)r= ∑∑ +j = - m

jj

i

i = 0i rArA

(Integer Portion) + (Fraction Portion)

i = n - 1 j = - 1

24

Decimal Number SystemBase (also called radix) = 10

● 10 digits { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }

Digit Position● Integer & fraction

Formal Notation

Digit Weight● Weight = (Base) Position

Magnitude● Sum of “Digit x Weight”

1 0 -12 -2

5 1 2 7 4

10 1 0.1100 0.01

500 10 2 0.7 0.04

d2*B2+d1*B

1+d0*B0+d-1*B

-1+d-2*B-2

(512.74)10

25

Octal Number SystemBase = 8

● 8 digits { 0, 1, 2, 3, 4, 5, 6, 7 }

Weights● Weight = (Base) Position

Formal Notation

Magnitude● Sum of “Digit x Weight”

1 0 -12 -2

8 1 1/864 1/64

5 1 2 7 4

5 *8 2+1 *8 1+2 *8 0+7 *8- 1+4 *8 -2

=(330.9375)10

(512.74)8

26

Octal Number System: Example

For Example, (27)8 can be expressed as: ( )10

(2 x 81) + (7 x 80 ) (2 x 8) + (7 x 1) 16 + 7 = (23)10

(17.1)8 can be expressed as: ( )10

(1 x 81) + (7 x 80) + (1 x 8-1) 8 + 7 + 0.125 (15.125)10

27

Hexadecimal Number System

Base = 16 ● 16 digits { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F }

Weights● Weight = (Base) Position

Formal Notation

Magnitude● Sum of “Digit x Weight”

1 0 -12 -2

16 1 1/16256 1/256

1 E 5 7 A

1 *162+14 *161+5 *160+7 *16-1+10 *16-2

=(485.4765625)10

(1E5.7A)16

10 12 13 151411

28

Hex to Decimal

Just multiply each hex digit by decimal value, and add the results.

163 162 161 160

4096 256 16 1

(2 a c)16

2 • 16 + 10 • 16 + 12 • 16 = (684)10

Dec Hex0 01 12 23 34 45 56 67 78 89 910 a11 b12 c13 d14 e15 f

2 1 0

Position 2 1 0

Binary Numbers

30

Binary Number System

Base = 2

● 2 digits { 0, 1 }, called binary digits or “bits”

Weights● Weight = (Base) Position

Magnitude● Sum of “Bit x Weight”

Formal Notation

Groups of bits 4 bits = Nibble

8 bits = Byte

1 0 -12 -2

2 1 1/24 1/4

1 0 1 0 1

1 *22+0 *21+1 *20+0 *2-1+1 *2-2

=(5.25)10

(101.01)21 0 1 1

1 1 0 0 0 1 0 1

31

Binary → Decimal: Example

7 6 5 4 3 2 1 0

27 26 25 24 23 22 21 20

128 64 32 16 8 4 2 1

1 0 0 1 1 1 0 0

128 + 0 + 0 + 16 + 8 + 4 + 0 + 0 = (156)10

What is (10011100)2 in decimal?7 6 5 4 3 2 1 0 position

Binary #

position

value

32

Binary Numbers Examples:

(00)2 (0)10 (01)2 (1)10 (0000001)2 (1)10 (10)2 (2)10 (010)2 (2)10 (11)2 (3)10 (100)2 (4)10 (1001010101000)2

Strings of binary digits (“bits”)One bit can store a number from 0 to 1 n bits can store numbers from 0 to 2n-1

33

Binary Fractions

bi bi-1 . . . b2 b1 b0 b-1 b-2 b-3 … b-j

1242i-12i

2-j

1/8

1/4

1/2

Integer Values

Fractional Values

decimal number =

34

Example 1: Binary to Decimal

(1 1 0 . 1 1)2

1 x 22 + 1 x 21 + 0x20 + 1x2-1 + 1x2-2

(6 and ¾)10

Position 2 1 0 -1 -2

35

Example 2: Binary to Decimal

(0 . 1 1 1 1 1 1)2

(63/64) 10

0 x 20 + 1 x 2-1 + 1x2-2 + 1x2-3 + 1x2-4 + 1x2-5 + 1x2-6

Note: (1) Numbers of the form 0.11111…2 are just below 1.0(2) Short form notation for such numbers is 1.0 - ε

Position 0 -1 -2 -3 -4 -5 -6

Why Binary?This is easier to implement in hardware than a unit

that can take on 10 different values.● For instance, it can be represented by a transistor being

off (0) or on (1).

● Alternatively, it can be a magnetic stripe that is magnetized with North in one direction (0) or the opposite (1).

Binary also has a convenient and natural association with logical values of:● False (0) and

● True (1).36

37

The Power of 2

n 2n

0 20=11 21=22 22=43 23=84 24=165 25=326 26=647 27=128

n 2n

8 28=2569 29=51210 210=102411 211=204812 212=409620 220=1M30 230=1G40 240=1T

Mega

Giga

Tera

Kilo

As n increasesby 1

2n doublesin value

ENG2410�Digital Design�“Introduction to Digital Systems: Part 1”TopicsResourcesSlide Number 4Computing Devices Everywhere!The Transistor RevolutionProcessor: Digital SystemSlide Number 8Slide Number 9Transistor as a SwitchnMOS TransistorSlide Number 12Slide Number 131.3VLSI Design StylesSlide Number 15SignalsSignalsAnalog SignalsDigital SignalsDigital: Sync vs. AsyncBinary Values: Other Physical QuantitiesSlide Number 22Number Systems – RepresentationDecimal Number SystemOctal Number SystemOctal Number System: ExampleHexadecimal Number SystemHex to DecimalSlide Number 29Binary Number SystemBinary Decimal: ExampleBinary NumbersSlide Number 33Slide Number 34Slide Number 35Why Binary?The Power of 2 Slide Number 38