ESZC261-L1

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BITS PilaniPilani Campus

BITS Pilanipresentation

Rekha.AFaculty

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BITS Pilani, Pilani Campus

Course Outline

Digital design basics and number systems Binary logic gates Boolean algebra and K-map simplification

Arithmetic logic units Flip-flops Registers and counters

Introduction to microprocessors Architecture Instruction set and programming Memory and I/O interfacing Examples of system design

ESZC261 Digital Electronics and Microprocessors

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In Science , Technology, business we are constantly dealing with the quantities.

Quantities are measured, monitored, recorded etc. It is important that we be able torepresent their values efficiently and accurately.

Two basic ways of representing the numerical values of the quantity: Analog andDigital.

Analog representation of a quantity is represented by a voltage , current or meter movement that is proportional to the value of the quantity. Analog quantities canvary over a continuous range of values.

In digital representation the quantities are represented by symbols called digits. It isdiscrete.

Many number system are in use in Digital technology.

Decimal, Binary, Octal and Hexadecimal.

Digital systems and Binary numbers

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Decimal system : Composed of 10 numerals or symbols i.e 0,1,2,3,4,5,6,7,8,9. Alsocalled base 10 system.

In decimal system the value of the digit depends on its position . eg: 3763 carries most weight and hence called MSD, 6 carries least weight and hencecalled LSD.

Binary system , there are only two symbols 0 &1. It is also called as base 2.

Octal System : Composed of 8 symbols i.e 0-7

Hexadecimal System ; Composed of 16 symbols i.e 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F.

Topic: Number systems and codes.

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Digital System Takes a set of discrete information inputs and discrete internal

information (system state) and generates a set of discrete

information outputs .

System State

DiscreteInformationProcessingSystem

DiscreteInputs Discrete

Outputs


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Types of Digital Systems


No state present Combinational Logic System Output = Function(Input)

State present State updated at discrete times=> Synchronous Sequential System

State updated at any time=>Asynchronous Sequential System

State = Function (State, Input) Output = Function (State)

or Function (State, Input)

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A Digital Computer Example


Memory

Controlunit Datapath

Input/Output

CPU

Inputs:Keyboard,

mouse, modem,microphone

Outputs: CRT,LCD, modem,

speakers

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Signal


An information variable represented by physical quantity.For digital systems, the variable takes on discrete values.Two level, or binary values are the most prevalent values indigital systems.

Binary values are represented abstractly by: digits 0 and 1 words (symbols) False (F) and True (T) words (symbols) Low (L) and High (H) and words On and Off.

Binary values are represented by values or ranges of values of physical quantities

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Signal Examples Over Time

Analog

Asynchronous

Synchronous

TimeContinuousin value &

timeDiscrete in

value &continuous

in timeDiscrete in

value &time

Digital

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Binary to Decimal

Binary number system is a positional system

Illustration 1:1 1 0 1 1 (binary)

24 + 2 3 + 2 2 + 2 1 + 2 0 = 16+8+2+1=27 10 (Decimal)

Illustration 21 0 1 1 0 1 0 1 (Binary)27 + 2 6 + 2 5 + 2 4 + 2 3 + 2 2 + 2 1 + 2 0 = 181(Decimal)


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Decimal to Binary : Conversion can be done by repeatedly dividing the decimalnumber by 2.

Illustration 1;Convert the decimal number 25 to binary

25/2 = 12 + remainder of 1

12/2 =6 + remainder of 06/2 = 3 + remainder of 03/2= 1 + remainder of 1(25) 10 = (11001) 2

Illustration 2:Convert the decimal number 37 to Binary

37/2 = 18 + remainder of 118/2 = 9 + remainder of 09/2 = 4 + remainder 14/2 =2 + remainder 02/2 = 1 + remainder 0(37) 10 = (100101) 2


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Octal Number systemOctal to decimal conversion: An octal number can be converted to its decimal

equivalent by multiplying each octal digit by its positional weight.Example:

372 8 = 3*82 + 7*81 + 2*80

= 3*64 + 7*8 + 2*1=250 10

Decimal to Octal A decimal integer can be converted to octal by repeated division by 8Example:

Convert the decimal number 266 to Octal266/8 = 33 + remainder 233/8 = 4 + remainder 1266 10 = 412 8


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Octal to Binary conversionThe primary advantage of the octal number is the ease with which theconversion can be made between the binary and the octal number Example: Convert the octal number 472 to binary

4 7 2100 111 010

472 8 = 100111010 2

Example 2: Convert the octal number 2435 to binary2 4 3 5010 100 011 1012435 8 = 010100011101 2


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Binary to Octal

Example: Convert the Binary number 100111010 to octal100 111 0104 7 2

100111101 2 = 472 8Usefulness of octal system: when dealing with a large quantity of binary

numbers of many bits, it is convenient and more efficient to write numbers inoctal.


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HEXADECIMAL NUMBER SYSTEM

Hex to decimal conversion

Example: Convert the (2AF) 16 to decimal

(2AF)16 = 2*16 2 + 10*16 1+ 15*16 0= 512+160+15

= 687 10

Decimal to HEX conversion

Example: Convert 423 10to HEX423/16 = 26 + remainder 726/16 = 1 + remainder 10423 10 = 1A7 16


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Binary to HEX Conversion

Example: Convert (1110110010011110) 2 to HEX1110 1100 1001 1110

D C 9 D

1110110010011110 2 = DC9D 16

HEX to Binary

Example: Convert ( AFE5) 16 to Binary A F E 51010 1111 1110 0101

AFE5 16 = 1010111111100101 2


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HEX to OCTAL conversion

Example: Convert B2F 16 to octal

B2F 16 = 1011 0010 1111 (convert to binary)= 101 100 101 111 (group into 3 bit groupings)

= 5 4 5 7 (convert to octal)


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BCD CodeIf each digit of the decimal number is represented by its binary equivalent , the result is a

code called Binary coded Decimal (BCD). Since a decimal digit can be as large as 9,four bits are required to code each digit.

Suppose ,6 3 8 (Decimal)0110 0011 1000 (BCD)

ASCII ( American Standard code for Information Interchange)

The ASCII code is a 7 bit code, so it has 27 possible code groups. This is more thanenough to represent all the standard keyboard characters as well as the controlfunctions such as , . The ASCII code is used for thetransfer of alphanumeric information between a computer and the input/outputdevices.


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American standard Code for Information Interchange(ASCII)

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Example1: Encode the following message in ASCII code using the HEX representation :COST = $72

Solution : 43 ,4F , 53,54, 20, 3D, 20, 24, 37, 32

Example 2:

The following ASCII coded message is stored in successive memory locations in a computer1010011 1010100 1001111 1010000

What is the message?

Ans: STOP


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GRAY CODE

The output data of many physical systems are quantities that are continuous

The data must be converted to digital form before they are applied to the digitalsystem

The Advantage of the gray code over the straight binary code is that only one bit inthe code group changes in going from one number to the next number.

Gray code is also referred to as the reflected code

The gray code is used in applications in which normal sequence of binary numbersmay produce an error or ambiguity during the transition from one number toanother.

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Parity method for error detection

The movement of binary data and codes from one location to another is themost frequent operation performed in the digital system.

When ever the information is being transmitted from one device to another,there is possibility that error can occur such that the receiver does notreceive the identical information that was sent.

For this reason digital systems employ some method for detection of errors.

One of the simplest and most widely used schemes for error detection is theparity method.


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A parity bit is an extra bit that is attached to a code group that is beingtransferred from one location to another. The parity bit is made either 1 or 0.

In the even parity method, the value of the parity bit is chosen so that thetotal number of 1s in the code (including the parity bit) is an even number. If the code is 1000011, the new code group including the parity bit becomes,11000011.

The odd parity method is used exactly the same way except that the paritychosen so that total no. of 1s is an odd number. If suppose the code is1000010, then the code after the parity it is added becomes 11000010.

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Example 1: Attach an odd parity bit to the ASCII code for the $ symbol andexpress the result in hex decimal.

Solution: The 7 Bit ASCII code for symbol $ is 010 0100

For odd parity the code becomes 1010 0100,

Therefore Hexa decimal representation becomes A4.

Example 2: Attach an even parity bit to the BCD code for decimal 69,

Solution: BCD code for decimal 69 is 01101001 After adding the even parity the code becomes 001101001


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ESZC261-L1