Digital Fundamentals Tenth Edition Floyd © 2008 Pearson Education Chapter 1

What you will Learn in this Course? Towards the end of this course, you should be able to: –Carry out arithmetic computation in various number systems –Apply rules of Boolean algebra to simplify Boolean expressions –Translate Boolean expressions into equivalent truth tables and logic gate implementations and vice versa –Design efficient combinational and sequential logic circuit implementations from functional description of digital systems –Carry out simple CAD simulations to verify the operation of logic circuits

Is it Worth the Effort? Absolutely! Digital circuits are employed in the design of: –Digital computers –Data communication –Digital phones –Digital cameras –Digital TVs, etc. This course presents the basic tools for the design of digital circuits and provides the fundamental concepts used in the design of digital systems

Which Book will be Used? “Digital Fundamentals”, Thomas L. Floyd. Pearson Prentice Hall, Ninth Edition. ISBN:

Grading Policy Assignments & Quizzes 15% Project 10% Midterm Exam 25% Final Exam 50%  NO makeup exam will be given whatsoever

Introduction Digital is derived from the way computers perform operations, by counting digits. In past digital electronics confined to computer systems. Today, digital technology every where.. TV, radar, medicine, communication, military, transportation..

Most natural quantities that we see are analog and vary continuously. Analog systems can generally handle higher power than digital systems. Digital systems can process, store, and transmit data more efficiently but can only assign discrete values to each point. Analog Quantities

Are computers analog or digital systems? Computer are digital systems Which is easier to design an analog or a digital system? Digital systems are easier to design, because they deal with a limited set of values rather than an infinitely large range of continuous values The world around us is analog It is common to convert analog parameters into digital form This process is called digitization Analog v/s Digital System

Many systems use a mix of analog and digital electronics to take advantage of each technology. A typical CD player accepts digital data from the CD drive and converts it to an analog signal for amplification. Analog and Digital Systems

Many systems use a mix of analog and digital electronics to take advantage of each technology. A typical CD player accepts digital data from the CD drive and converts it to an analog signal for amplification. Analog and Digital Systems

Analog-to-Digital Converter (ADC) Produces digitized version of analog signals Analog input => Digital output Digital-to-Analog Converter (DAC) Regenerate analog signal from digital form Digital input => Analog output Our focus is on digital systems only Both input and output to a digital system are digital signals ADC and DAC Converters Analog-to-Digital Converter (ADC) Digital-to-Analog Converter (DAC) Digital System input digital signals output digital signals input analog signals output analog signals

Processed more efficiently and reliably Compact storage Greater accuracy Does not affected by noise as well as analog values Digital Advantages:

Digital electronics uses circuits that have two states, which are represented by two different voltage levels called HIGH and LOW. The voltages represent numbers in the binary system. Binary Digits and Logic Levels HIGH = 1 =True LOW = 0 = False

Digital electronics uses circuits that have two states, which are represented by two different voltage levels called HIGH and LOW. The voltages represent numbers in the binary system. Binary Digits and Logic Levels In binary, a single number is called a bit (for binary digit). The value of a bit is either 0 or 1, corresponding to signal voltage LOW or HIGH, respectively (example). HIGH LOW V H(max) V H(min) V L(max) V L(min) Invalid

Digital waveforms change between the LOW and HIGH levels. A positive going pulse is one that goes from a normally LOW logic level to a HIGH level and then back again. Digital waveforms are made up of a series of pulses. Digital Waveforms

Actual pulses are not ideal but are described by the rise time, fall time, amplitude, and other characteristics. Pulse Definitions

Periodic pulse waveforms are composed of pulses that repeat at fixed intervals (period). The frequency is the rate at which the pulses repeat; measured in Hertz. Periodic Pulse Waveforms

Periodic pulse waveforms are composed of pulses that repeat at fixed intervals (period). The frequency is the rate at which the pulses repeat; measured in Hertz. Periodic Pulse Waveforms The clock is a basic timing signal that is an example of a periodic wave. What is the period of a repetitive wave if f = 3.2 GHz? 313 ps

Pulse Definitions In addition to frequency and period, repetitive pulse waveforms are described by the amplitude (A), pulse width (t W ) and duty cycle. Duty cycle is the ratio of t W to T. Amplitude (A) Pulse width (t W ) Period, T

Pulse Definitions In addition to frequency and period, repetitive pulse waveforms are described by the amplitude (A), pulse width (t W ) and duty cycle. Duty cycle is the ratio of t W to T. Duty Cycle = (t W / T)*100% = (1ms / 10ms)*100%= 10%

A timing diagram is used to show the relationship between two or more digital waveforms, Timing Diagrams A diagram like this can be observed directly on a logic analyzer.

Data can be transmitted by either serial transfer or parallel transfer. Serial and Parallel Data

Basic Logic Functions True only if all input conditions are true. True only if one or more input conditions are true. Indicates the opposite condition.

n-input Gates Because + and * are binary operations, they can be cascaded together to OR or AND multiple inputs. A B C A+B+C A B C A B ABC C A B C

n-input Gates For convenience, it is sometimes useful to think of the logic gates processing n-bits at a time. This really refers to n instances of the logic gate, not a single logic date with n- inputs

Basic System Functions And, or, and not elements can be combined to form various logic functions. A few examples are: The comparison function Basic arithmetic functions

Basic System Functions The encoding function The decoding function

Basic System Functions The data selection function

Basic System Functions The counting function …and other functions such as code conversion and storage. Input pulses 1 CounterParallel output lines Binary code for 1 Binary code for 2 Binary code for 3 Binary code for 4 Binary code for 5 Sequence of binary codes that represent the number of input pulses counted. 2345

Basic System Functions One type of storage function is the shift register, that moves and stores data each time it is clocked.

Integrated Circuits Cutaway view of DIP (Dual-In-line Pins) chip: The TTL series, available as DIPs are popular for laboratory experiments with logic.

An example of laboratory prototyping is shown. The circuit is wired using DIP chips and tested. Integrated Circuits In this case, testing can be done by a computer connected to the system. DIP chips

Integrated Circuits DIP chips and surface mount chips Pin 1 Dual in-line package Small outline IC (SOIC)

Integrated Circuits Other surface mount packages: SOIC PLCC LCCC

Test and Measurement Instruments The front panel controls for a general-purpose oscilloscope can be divided into four major groups.

Test and Measurement Instruments For measuring digital signals, use DC coupling Normally, trigger on the slower of two waveforms when comparing signals.

Test and Measurement Instruments The logic analyzer can display multiple channels of digital information or show data in tabular form.

Test and Measurement Instruments 0.01 V The DMM can make three basic electrical measurements. Voltage Resistance Current In digital work, DMMs are useful for checking power supply voltages, verifying resistors, testing continuity, and occasionally making other measurements.

Programmable Logic Programmable logic devices (PLDs) are an alternative to fixed function devices. The logic can be programmed for a specific purpose. In general, they cost less and use less board space than fixed function devices. A PAL device is a form of PLD that uses a combination of a programmable AND array and a fixed OR array:

Analog Digital Binary Bit Pulse Being continuous or having continuous values. Related to digits or discrete quantities; having a set of discrete values. Having two values or states; describes a number system that has a base of two and utilizes 1 and 0 as its digits. A binary digit, which can be a 1 or a 0. A sudden change from one level to another, followed after a time, called the pulse width, by a sudden change back to the original level.

Clock Gate NOT AND OR A basic timing signal in a digital system; a periodic waveform used to synchronize actions. A logic circuit that performs a basic logic operations such as AND or OR. A basic logic function that performs inversion. A basic logic operation in which a true (HIGH) output occurs only when all input conditions are true (HIGH). A basic logic operation in which a true (HIGH) output occurs when when one or more of the input conditions are true (HIGH).

Fixed-function logic Programmable logic A category of digital integrated circuits having functions that cannot be altered. A category of digital integrated circuits capable of being programmed to perform specified functions.

SELF TEST

Assignment No 1 Learning Activity Study different types of number systems –Binary –Decimal –Octal –Hexadecimal