CoE 111Logic Circuits and Switching Theory

Module 1Review on Digital Circuits

Objectives

Review on Digital LogicIntroduction Digital computers have made possible many scientific, industrial, and commercial advances that would have been unattainable otherwise. Our space program would have been impossible without real time, continuous computer monitoring, and many business enterprises function efficiently only with the aid of automatic data processing.

Logic Design vs. Computer Design• Logic design – deals with the basic

concepts and tools used to design digital hardware consisting of logic circuits.

• Computer design – deals with additional concepts and tools used to design computers and other complex digital hardware.

Numerical Representations• Almost all the fields of endeavor are

dealing with quantities.

• Quantities – are measured, monitored, recorded, manipulated arithmetically, observed, and utilized in most physical systems.

• There is a need to represent these quantities/values efficiently and accurately.

Ways to represent numerical values• Analog representation – represented by

a voltage, current, or meter movement proportional to the value of that quantity.

• Digital representation –represented not by continuously variable indicators but by symbols called digits.

Analog Examples:• Automobile speedometer

—deflection of the needle is proportional to the speed of the auto.

• Mercury thermometer —height of the column of mercury is proportional

to the room temperature.• Audio microphone

—output voltage is generated in proportion to the amplitude of the sound waves that impinge on the microphone.

• Analog AC-powered wall clock —time of the day changes continuously as the

needle reading changes continuously.

Analog Signal Characteristics• Having a continuous range of values and

can be associated with continuous physical phenomena.

• Continuous signal - smooth connected, an unbroken series of consecutive values with no instantaneous changes.

+5

V

–5 T ime

Digital Example• Digital watch

—provides time of the day in the form of digital digits that represents hours and minutes (and sometimes seconds).

—The watch reading changes in discrete steps of one per minute (or per second).

Digital signal• Typically has two discrete values (or

states) and are appropriate for any phenomena involving counting or integer numbers.

• Discrete signal - separated into distinct segments or pieces, a series of discontinuous values.

+5

V

–5

1 0 1

T ime

Major differences:Analog and Digital quantities:

• Analog continuously variable defined values

• Digital vary only by discrete steps

Analog DigitalContinuously variable Discrete stepsAmplification SwitchingVoltages Numbers

Major differences:Analog and Digital quantities:

• No ambiguity in reading the value of a digital quantity

• Value of analog quantity is often open to interpretation, thus we always “round” to a convenient level of precision.

Points to Ponder: • Real life is full of analog signals.• Analog systems: slight error in input, large

error in output.• General purpose computers: digital• Sensors & actuators - interface circuits are

often analog.• Digital systems: more accurate, reliable

and deal better with degraded signals.• Digital signals - easier to process, used as

an approximation to real analog signals.

Points to Ponder:• Binary digital systems - has only two

discrete values that make digital systems easier to decode.

• Two discrete values:1. High voltage, high current flowing, ON,

TRUE, YES, "1"2. Low voltage, low current flowing, OFF,

FALSE, NO, "0"

Digital logic levels• Voltage that represents a defined digital

state in an electronic circuit.

• Logic LOW (or logic 0) —lower of two voltages (usually 0V) in a digital

system with two logic levels.• Logic HIGH (or logic 1)

—higher of two voltages (traditionally 5V, but in some systems a specific value such as 1.8V, 2.5V or 3.3V) in a digital system with two logic levels.

Digital logic levels

+5V

+1.8V

+0.8V

0V

Logic HIGH

Logic LOW

Undefined

Digital System• Devices designed to manipulate logical

information or physical quantities that are represented in digital form.

• Most often electronic, but they can also be mechanical, magnetic, or pneumatic.

Video equipmentDigital audio

CalculatorDigital computer

Analog system • Devices that manipulate physical

quantities that are represented in analog form.

Speaker

Magnetic tape recording and playback equipment

Advantages of digital techniques • Reproducibility of results • Easier to design • Flexibility and functionality • Programmability • Speed • Economy • Steadily advancing technology • Storage is easy

Limitations of Digital Techniques • The real world is analog – most physical

quantities are analog in nature.

• Processing digitized signals takes time.

Digital Conversion:• when dealing with analog inputs and

outputs:—Convert the real-world analog inputs to digital

form.—Process (or operate on) the digital information—Convert the digital outputs back to real-world

analog form.

Block diagram

Measuring device

Analog-to-digital

converterDigital

processing

Analog-to-digital

converterController

Temperature(Analog) (Analog) (Digital)

(Digital)

(Analog)Adjust

temperature

Digital Circuit• Inherently binary in nature, but several

types of representations of numerical data are in use.

• The representation of an unsigned integer can be done in binary, octal, decimal or hexadecimal.

• For display purposes, each decimal digit is often represented by a four-bit binary number in a system called binary coded decimal (BCD).

Digital Representation