Chapter 2:Chapter 2:Fundamentals of Fundamentals of Digital ElectronicsDigital Electronics

Dr Mohamed MenacerDr Mohamed MenacerTaibah UniversityTaibah University

2007-20082007-2008

AbstractAbstract

• The basics of Boolean algebra will be introduced, starting from simple combinational logic functions and basic sequential logic circuits such as latches and flip-flops. • Transistor basics will be reviewed and circuits introduced that demonstrate implementations of the basic logic elements in TTL/CMOS technology. • Based on these fundamentals, more complex logic structures such as decoders, adders, registers, and memories will constructed and their performance analyzed. • The logic functions used as the architectural basis for programmable devices used in spaceborne electronics will be examined and analyzed.

OutlineOutline

IntroductionIntroduction

Basic LogicBasic Logic

Hardware (Transistors, Gates)Hardware (Transistors, Gates)

Combinational LogicCombinational Logic

Sequential LogicSequential Logic

Module Design in Programmable DevicesModule Design in Programmable Devices

Basic Digital LogicBasic Digital Logic

Logic ValuesLogic Values

For binary hardwareFor binary hardware Either a ‘1’ or a ‘0’Either a ‘1’ or a ‘0’ ““Most of the time”Most of the time”

Other types of hardware can be have Other types of hardware can be have more than two valuesmore than two values

Simulation can use a multi-value logic Simulation can use a multi-value logic systemsystem VHDL Std_Logic uses a nine-valued logicVHDL Std_Logic uses a nine-valued logic

Binary Hardware Logic ValuesBinary Hardware Logic Values

Logic ‘1’Logic ‘1’

Logic ‘0’Logic ‘0’

Undefined valueUndefined value

TTL Logic LevelsTTL Logic Levels

Logic ‘1’ threshold - VLogic ‘1’ threshold - VIHIH

2.0 V2.0 V

Logic ‘0’ threshold - VLogic ‘0’ threshold - VILIL

0.8 V0.8 V

UndefinedUndefined0.8 V < v < 2.0 V0.8 V < v < 2.0 V

TTL Logic LevelsTTL Logic LevelsExamples of Undefined Examples of Undefined

ValuesValuesFloating signals may take on illegal valuesFloating signals may take on illegal values

What happens during a signal transition?What happens during a signal transition?

0.8V

2.0V

Logic ‘0’

Undefined

Logic ‘1’

Logic Values and Basic Logic Values and Basic FunctionsFunctions

Logic ValuesLogic Values

LevelsLevels '0' or '1''0' or '1'

PulsesPulses Presence or absence of pulsesPresence or absence of pulses Pulse widthsPulse widths Number of pulsesNumber of pulses

Zero crossingsZero crossings

5Digital Waveform

Time

Vol

tage

(V

) 1

0

1

Switching AlgebraSwitching Algebra

Two-valued variable from {0,1}Two-valued variable from {0,1}

Two binary operationsTwo binary operations AND ( • )AND ( • ) OR ( + )OR ( + )

One unary operationOne unary operation NOT ( NOT ( ) )

Unary Operation - NOTUnary Operation - NOT

A Y

0 1

1 0

NOT OperatorTruth Table

A B

The NOT gate reverses the inputThe NOT gate reverses the input

Binary Operation - ANDBinary Operation - AND

A B Y

0 0 0

0 1 0

1 0 0

1 1 1

AND means that both AND means that both conditions must be conditions must be truetrue in order in order for the conclusion to be for the conclusion to be truetrue

AInputs

B

Output

Binary Operation - [Inclusive] Binary Operation - [Inclusive] OROR

A B Y

0 0 0

0 1 1

1 0 1

1 1 1

Another basic operator is the ORAnother basic operator is the OROR works such that the output is OR works such that the output is truetrue, if either of the two inputs is , if either of the two inputs is truetrue

DigitalDigital XORXOR

We can build an electrical device that performs the logical We can build an electrical device that performs the logical XOR operation on voltage equivalents of logic valuesXOR operation on voltage equivalents of logic values

An XOR gate has the An XOR gate has the electrical schematic:electrical schematic:

XOR OperatorTruth Table

0 0 0A B Output

0 1 11 0 11 1 0

A

InputsOutput

B

All digital computers are built All digital computers are built using only three gate types: using only three gate types:

AND, OR, and NOTAND, OR, and NOT

TransistorsTransistors

Transistor DefinitionsTransistor Definitions

MOS - Metal Oxide SemiconductorMOS - Metal Oxide Semiconductor

FET - Field Effect TransistorFET - Field Effect Transistor

BJT - Bipolar Junction TransistorBJT - Bipolar Junction Transistor

TransistorTransistor

npn bipolar transistor

collector

base

emitter

NAND

NOR NOT