Binary Numbers and Binary Numbers and ASCII and EDCDICASCII and EDCDIC

Mrs. CueniMrs. Cueni

Data RepresentationData Representation

Human speech is analog because it uses Human speech is analog because it uses continuous signals (waves) that vary in continuous signals (waves) that vary in strength and qualitystrength and quality

Computers are digital – recognize two Computers are digital – recognize two states ones and zeros, on of offstates ones and zeros, on of off

0 and 1 is called a bit 0 and 1 is called a bit BBinary Diginary Digitit Smallest unit of informationSmallest unit of information

Data representationData representation

8 bits grouped together called a byte8 bits grouped together called a byte Represent 256 individual charactersRepresent 256 individual characters Numbers, uppercase, lowercase letters, Numbers, uppercase, lowercase letters,

punctuation markspunctuation marks Based 2 numbering systemBased 2 numbering system

Coding SchemeCoding Scheme

Two popular coding schemesTwo popular coding schemes ASCII – American Standard Code for ASCII – American Standard Code for

Information InterchangeInformation Interchange EBCDIC – Extended Binary Coded Decimal EBCDIC – Extended Binary Coded Decimal

Interchange CodeInterchange Code Sufficient for English and Western Europe Sufficient for English and Western Europe

languageslanguages Not large enough for Asian and other Not large enough for Asian and other

languageslanguages

Coding Sheet ASCII numbersCoding Sheet ASCII numbers 00110000 is the number zero00110000 is the number zero The first four bits 0011 – identify as a The first four bits 0011 – identify as a

numbernumber The last four digits 0000 determines the The last four digits 0000 determines the

numbernumber

128 64 32 16 8 4 2 1

0 0 1 1 0 0 0 0

Binary numbering systemBinary numbering system

Base 10Base 10

4+2+1 = 74+2+1 = 7

Base 2Base 2

4+2+1 = 7

8+2 = 10

27 26 25 24 23 22 21 20

128 64 32 16 8 4 2 1

0 0 1 1 0 1 1 1

0 0 1 1 1 0 1 0

107 106 105 104 103 102 101 100

10000000 1000000 100000 10000 1000 100 10 1

8 5 6 8 0 3 4 5 85,680,345

What are these numbers?What are these numbers?

00110101 – 00110101 –

What are these numbers?What are these numbers?

00110011 –00110011 –

What are these numbers?What are these numbers?

00111001 –00111001 –

What are these numbers?What are these numbers?

00110111 –00110111 –

What are these numbers?What are these numbers?

00110110 –00110110 –

What are these numbers?What are these numbers?

0011111100111111

Coding Sheet ASCII lettersCoding Sheet ASCII letters

01000001 is the letter A01000001 is the letter A The first two bits 01 – identify as a letterThe first two bits 01 – identify as a letter The last six digits 000001 determines the The last six digits 000001 determines the

letter as the first letter in the alphabet Aletter as the first letter in the alphabet A

How did you do that?How did you do that?

01011010 is the letter Z01011010 is the letter Z The first two bits 01 – identify as a letterThe first two bits 01 – identify as a letter The last digits 011010 = 16+8+2=26The last digits 011010 = 16+8+2=26 2626thth letter Z letter Z

128 64 32 16 8 4 2 1

0 1 0 1 1 0 1 016+8+2=26

Letter orderLetter order

11stst – A – A 22ndnd – B – B 33rdrd – C – C 44thth – D – D 55thth – E – E 66thth – F – F 77thth- G- G 88thth – H – H

99thth - I - I 1010thth – J – J 1111thth – K – K 1212thth – L – L 1313thth- M- M 1414thth – N – N 1515thth- O- O 1616thth - P - P

1717thth – Q – Q 1818thth – R – R 1919thth – S – S 2020thth – T – T 2121stst – U – U 2222ndnd - V - V 2323rdrd – W – W 2424thth – X – X

25th – Y

2626thth - Z

What are these letters?What are these letters?

0100000101000001 0101011101010111 0100101001001010 0101010101010101

Coding SchemesCoding Schemes

Make it possible to interact with computersMake it possible to interact with computers Does this very quickly without you Does this very quickly without you

realizing itrealizing it Type a character, the computer converts it Type a character, the computer converts it

and processes the data to something it and processes the data to something it understandsunderstands

The software converts it back to The software converts it back to something we understandsomething we understand

UnicodeUnicode

Many languages use symbols called Many languages use symbols called ideograms to represent multiple words or ideograms to represent multiple words or ideasideas

Unicode is a 16-bit code that has the Unicode is a 16-bit code that has the capacity of representing more than 65,000 capacity of representing more than 65,000 characters and symbolscharacters and symbols

Parity bitParity bit

Used by computers for error checkingUsed by computers for error checking Extremely rareExtremely rare Computers are either odd- or even- parityComputers are either odd- or even- parity Total number of bits on must be even on Total number of bits on must be even on

even-parity computers or odd on odd-even-parity computers or odd on odd-parity bit computersparity bit computers

9 bit pattern9 bit pattern

Transferring dataTransferring data

When computers transfer data from one When computers transfer data from one location to another it checks the sending location to another it checks the sending data and the receiving data to make sure data and the receiving data to make sure the parity bit is the samethe parity bit is the same

An error is displayed if the parity doesn’t An error is displayed if the parity doesn’t matchmatch

HexadecimalHexadecimal

Used for communicating with Used for communicating with programmers when a problem existsprogrammers when a problem exists

0’s and 1’s can be difficult to read0’s and 1’s can be difficult to read Pass out Hexadecimal chartPass out Hexadecimal chart

HexadecimalHexadecimal Uses 16 symbols to represent valuesUses 16 symbols to represent values Hex means six, deci means tenHex means six, deci means ten Conversion between binary and hexadecimal is Conversion between binary and hexadecimal is

very efficientvery efficient The letter M is 01001101 in binaryThe letter M is 01001101 in binary In Hexadecimal 4DIn Hexadecimal 4D Divide binary number into two sections 0100 and Divide binary number into two sections 0100 and

11011101 Convert each section to the hex equivalent 0100 Convert each section to the hex equivalent 0100

is a 4 and 1101 is letter Dis a 4 and 1101 is letter D A=10, B=11, C=12, D=13, E=14, F=16A=10, B=11, C=12, D=13, E=14, F=16

Data Storage videoData Storage video

Progressive Insurance video on data Progressive Insurance video on data storagestorage

Binary Conversion SheetBinary Conversion Sheet

Complete in class the binary conversion Complete in class the binary conversion sheetsheet

Worth 26 pointsWorth 26 points

SourcesSources

http://www.computerhope.com/binhex.htm