DataRepresentation,Types&Conversions

RepresentationSchemes•  UnsignedMagnitude•  SignedMagnitude•  One’scomplement•  Two’scomplement

Unsignedmagnitude•  Unsignedintegerscanrepresentzeroandposi9veintegers,butnotnega9veintegers.•  Example1:Supposethatn=8andthebinarypaFernis01000001,thevalueofthisunsignedintegeris1×2^0+1×2^6=65.•  Example2:Supposethatn=16andthebinarypaFernis0001000000001000,thevalueofthisunsignedintegeris1×2^3+1×2^12=4104.•  Ann-bitpaFerncanrepresent2^ndis9nctintegers.•  Ann-bitunsignedintegercanrepresentintegersfrom0to(2^n)-1

Signedmagnitude•  Themost-significantbit(msb)isthesignbit,withvalueof0represen9ngposi9veintegerand1represen9ngnega9veinteger.

•  Theremainingn-1bitsrepresentsthemagnitude(absolutevalue)oftheinteger.Theabsolutevalueoftheintegerisinterpretedas"themagnitudeofthe(n-1)-bitbinarypaFern".

Signedmagnitude•  Example1:Supposethatn=8andthebinaryrepresenta9onis01000001.Signbitis0⇒posi9veAbsolutevalueis1000001=65Hence,theintegeris+65

•  Example2:Supposethatn=8andthebinaryrepresenta9onis10000001.Signbitis1⇒nega9veAbsolutevalueis0000001=1Hence,theintegeris-1

Signedmagnitude•  Example3:Supposethatn=8andthebinaryrepresenta9onis00000000.Signbitis0⇒posi9veAbsolutevalueis0000000=0Hence,theintegeris+0

•  Example4:Supposethatn=8andthebinaryrepresenta9onis10000000.Signbitis1⇒nega9veAbsolutevalueis0000000B=0Hence,theintegeris-0

One’sComplement•  Themostsignificantbit(msb)isthesignbit,withvalueof0represen9ngposi9veintegersand1represen9ngnega9veintegers.•  Theremainingn-1bitsrepresentsthemagnitudeoftheinteger,asfollows:•  forposi9veintegers,theabsolutevalueoftheintegerisequalto"themagnitudeofthe(n-1)-bitbinarypaFern".•  fornega9veintegers,theabsolutevalueoftheintegerisequalto"themagnitudeofthecomplement(inverse)ofthe(n-1)-bitbinarypaFern"(hencecalled1'scomplement).

One’scomplement•  Example1:Supposethatn=8andthebinaryrepresenta9on01000001.Signbitis0⇒posi9veAbsolutevalueis1000001=65Hence,theintegeris+65

•  Example2:Supposethatn=8andthebinaryrepresenta9on10000001.Signbitis1⇒nega9veAbsolutevalueisthecomplementof0000001B,i.e.,1111110B=126Hence,theintegeris-126

Two’scomplement• Again,themostsignificantbit(msb)isthesignbit,withvalueof0represen9ngposi9veintegersand1represen9ngnega9veintegers.•  Theremainingn-1bitsrepresentsthemagnitudeoftheinteger,asfollows:•  forposi9veintegers,theabsolutevalueoftheintegerisequalto"themagnitudeofthe(n-1)-bitbinarypaFern".•  fornega9veintegers,theabsolutevalueoftheintegerisequalto"themagnitudeofthecomplementofthe(n-1)-bitbinarypaFernplusone"(hencecalled2'scomplement).

Two’scomplement•  Example1:Supposethatn=8andthebinaryrepresenta9on00000000.Signbitis0⇒posi9veAbsolutevalueis0000000=0Hence,theintegeris+0

•  Example2:Supposethatn=8andthebinaryrepresenta9on11111111.Signbitis1⇒nega9veAbsolutevalueisthecomplementof1111111Bplus1,i.e.,0000000+1=1Hence,theintegeris-1

Conversions•  8bit=1byte•  1024byte=1KB•  1024KB=1MB•  1024MB=1GB•  1024GB=1TB•  1024TB=1PB

•  Kilo(10^3),Mega(10^6),Giga(10^9),Tera(10^12),Peta(10^15),Exa(10^18)…

•  ClassExamples:•  2048bytes=……KB=…….Bit=……MB

Conversions• 

DataTypes•  Adatatypedefinesasetofvaluesthatavariablecanstorealongwithasetofopera8onsthatcanbeperformedonthatvariable.

•  Commondatatypesareinteger,character,andreal.

DataTypes

DataTypes

DataTypes•  BasicDatatype(Primary,fundamental)•  Integers,CharacterandFloa8ngpoint

DataTypes•  BasicDatatype(Primary,fundamental)•  Integers•  Signedandunsignedtypes

•  Signed–canstore+and–veintegers•  Unsigned–canstoreonly+veintegers

DataTypes•  BasicDatatype(Primary,fundamental)•  Signedtypeintegers•  int:-integersarewholenumbers,capabletostoring

numericvaluewithoutdecimalplaces.•  anynumberintherange-32768to32767(16-bit)•  Itoccupies2bytesofmemory(16-bit),4bytes(32-bit)•  Longint:-required4bytesofmemory(16-bit),8byte

(32-bit).•  Valuerangefrom-2147483648to2147483647(32-bit)•  Longintvariablecandeclare•  longinta,b;orlonga;

DataTypes•  BasicDatatype(Primary,fundamental)•  Signedtypeintegers•  Shortintegers:-needlessspaceinmemory(sameas

int)•  Shortintvariablecandelare•  shortinta;orinta;(botharesame)

DataTypes•  BasicDatatype(Primary,fundamental)•  Unsignedintegers•  unsignedintegers:-some8meifweknowinadvanced,

thevaluestoredinanintegervariableisalwaysbe+ve.•  Suchsitua8onswecandeclaredthevariableas

unsignedint•  TherangepermissibleintegervaluewillshiWfrom0to

65535iedoublethesizeofint•  Unsignedintegervariablecandeclare•  unsignedinta;orunsigneda;(botharesame)

DataTypes•  BasicDatatype(Primary,fundamental)•  Unsignedintegers•  unsignedshortintegers:-sameasunsignedint•  unsignedlongintegers:-•  Range0to42949672954(doublesizeoflongint)•  Unsignedlongintegervariablecandeclare•  unsignedlonginta;

DataTypes•  BasicDatatype(Primary,fundamental)•  Characters•  Signedandunsignedtypes•  Bothoccupy1byteofmemory•  Buthavingdifferentrange•  Signedcharissameasordinarycharandhasrange-128

to127•  Unsignedcharrangefrom0to255•  Example•  cnsignedchara;•  chara;

DataTypes•  BasicDatatype(Primary,fundamental)•  Floa8ngpoint

•  Afloatvariableoccupy4bytesofmemory•  Rangefrom3.4E-38to3.4E+38•  Doubleoccupy8bytesofmemory•  Rangefrom1.7E-308to1.7E+308•  Longdoubleoccupy10bytesofmemory•  Rangefrom3.4E-4932to3.4E+4932

DataTypes(16-bit)

DataTypes(32-bit)

MemoryAllocationofVariables

DataTypes•  UserDefinedDataType•  TypeDefini8on•  Enumerateddatatype•  Structure•  Union

DataTypes•  Deriveddatatype•  Array…•  Func8ons…•  Pointers…•  Reference…

DataTypes•  Emptydatatype•  void

EscapeSequenceEscapesequenceisusedintheprina()func9ontodosomethingtotheoutput.

DataRepresentation•  Dataondigitalcomputersisrepresentedasasequenceof0sand1s.Thisincludesnumericdata,text,executablefiles,images,audio,andvideo.

•  Datacanberepresentedusing2n•  Numericrepresenta9on•  Fixedpoint•  Floa9ngpoint

•  Nonnumericrepresenta9on

Drawbacks•  Thedrawbacksofsign-magnituderepresenta9onare:•  Therearetworepresenta9ons(00000000Band10000000B)forthenumberzero,whichcouldleadtoinefficiencyandconfusion.

•  Posi9veandnega9veintegersneedtobeprocessedseparately.

Review•  Char:8bits•  int:32bits(Itactuallydependsonmicroprocessor&opera9ngsystem)

•  Float:Usually32bits•  Double:64bits