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Number Systems
Number Systems
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Number Systems
l In every numbering system dig=
its
are written in columns. Each column represents a different
value.
l In the decimal system the
rightmost column represents the “ones”, the second to
last column the “tens” the third to last the “on=
e hundreds”.
l
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Number Systems
Decimal System: Base 10
• In t=
he
decimal system 10 digits are used to represent numbers: 0 1 2 3 4 5 6 7 8 9
• The top line shows how each column represents the =
base
to a certain power.
<=
span
style=3D'font-size:94%'>• The second=
line
indicated the actual values
• The third line shows how many discrete numbers can=
be
represented with that =
number
of columns.
• For example the decimal number
“34” represents 4 x1 and 3 x 10
• The number=
4672
represents: 2x1 + 7x10 + 6x1,000 and 4x10,000
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Number Systems
Binary System: Base 2
<=
span
style=3D'mso-special-format:bullet;position:absolute;left:-1.02%'>•<=
/span>In
the Binary system 2 digits are used to represent numbers: 0 and 1
• This is very practical for computer systems as a
switch can represent the two digits.
• For example the number 1010 represents: 0x1 + 1x=
2 +
0 x4 + 1 x 8 =3D 10 in decimal
• 1101 1011 represents 1x1 + 1x2 + 0 x4 + 1 x 8 + =
1x16
+ 0x32 + 0 x64 + 1 x 128 =3D “219” in decimal=
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Number Systems
Binary System
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Number Systems
Hexadecimal system: Base 16
<=
span
style=3D'font-size:75%'>l <=
span
style=3D'font-size:75%'>The hexadecimal system, HEX, uses 16 digits to rep=
resent
numbers:
<=
span
style=3D'font-size:80%'>– 0 1 2 3 4 5 6 7 8 9 A B C D E F
=
<=
span
style=3D'font-size:75%'>l <=
span
style=3D'font-size:75%'> For =
example
the number 7B represents: 11x1 + 7x16 =3D 123
l 4 digit binary numbers can represented by one HEX =
digit.
Therefore long binary numbers=
can
be easily represented by shorter HEX numbers.
<=
span
style=3D'font-size:75%'>l <=
span
style=3D'font-size:75%'>One 16 bit number can be represented by only 4 HEX
numbers.
<=
span
style=3D'font-size:75%'>l <=
span
style=3D'font-size:75%'>For example: Binary 1011 0000 0111 1100 translates=
to
HEX B07C
<=
span
style=3D'font-size:80%'>– 1100 2 =3D 1210 =3D C HEX
<=
span
style=3D'font-size:80%'>– 0111 2 =3D 710 =3D 7 HEX
<=
span
style=3D'font-size:80%'>– 0000 2 =3D 010 =3D 0 HEX
<=
span
style=3D'font-size:80%'>– 1011 2 =3D 1110 =3D B HEX
<=
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Number Systems
MIDI
l MIDI uses a 7 digit binary sy=
stem
to represent the values of most parameters (program,
volume, pan, modulation)
l 7bits can only represent values from 0 to 127
l Two sets of 7 digits can be u=
sed
for a total of 32768 discrete numbers – (Pitch Bend)
=
l MIDI Channel only has four bi=
ts
for a maximum possible 16 channels
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Number Systems
Digital Audio
l 8 bit can represent 256 discrete numbers
l 12 bit - 4096
l 16 bit - 65,536
l 20 bit - 1,048,576
l 24 bit – 16,777,216
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Click to edit Master text styles
Second level
Third level
Fourth level
Fifth level
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if( IsFramesMode() ) return
if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue
doc=3DPPTSld.document
var dir =3D doc.body.dir
if( dir !=3D "rtl" ) dir =3D "ltr";
doc.open()
doc.writeln('' + ENDSHOW_MESG + '
=
body>')
doc.close()
}
function SetSldVisited(){ GetSldList().mList[gCurSld-1].mVisited=3Dtrue }
function IsSldVisited(){ return GetSldList().mList[gCurSld-1].mVisited }
function hrefList( sldHref, visible, advDelay, advClk )
{
this.mSldHref=3D this.mNtsHref =3D sldHref
this.mOrigVis=3D this.mVis =3D visible
this.mVisited=3D false
this.mAdvDelay=3D advDelay
this.mAdvOnClk=3D advClk
}
function SldList(arr,curSld,fEnd)
{
this.mCurSld =3D curSld;
this.mList =3D new Array();
var idx =3D 1;
for(ii=3D0;ii 0) {
PushSldList(sldList,fEnd);
gCurSld =3D 1;
}
else
if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue
}
function PushSldList(arr,fEnd) {
var ii =3D gSldStack.length;
gSldStack[ii] =3D new SldList(arr,gCurSld,fEnd);
GoToSld( gSldStack[ii].mList[0].mSldHref );
}
function PopSldList() {
if (gSldStack[gSldStack.length-1].fEndShow)
EndShow()
else {
gCurSld =3D gSldStack[gSldStack.length-1].mCurSld;
gSldStack[gSldStack.length-1] =3D null;
gSldStack.length--;
var sldList =3D gSldStack[gSldStack.length-1];
GoToSld( sldList.mList[gCurSld - 1].mSldHref );
}
}
var custShowList=3Dnew Array();
function ImgBtn( oId,bId,w,action )
{
var t=3Dthis
t.Perform =3D _IBP
t.SetActive =3D _IBSetA
t.SetInactive=3D _IBSetI
t.SetPressed =3D _IBSetP
t.SetDisabled=3D _IBSetD
t.Enabled =3D _IBSetE
t.ChangeIcon =3D null
t.UserAction =3D action
t.ChgState =3D _IBUI
t.mObjId =3D oId
t.mBorderId=3D bId
t.mWidth =3D w
t.mIsOn =3D t.mCurState =3D 0
}
function _IBSetA()
{
if( this.mIsOn ) {
obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 )
obj.style.posTop=3D0
}
}
function _IBSetI()
{
if( this.mIsOn ) {
obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 )
obj.style.posTop=3D0
}
}
function _IBSetP()
{
if( this.mIsOn ) {
obj=3Dthis.ChgState( gShadowClr,gHiliteClr,2 )
obj.style.posLeft+=3D1; obj.style.posTop+=3D1
}
}
function _IBSetD()
{
obj=3Dthis.ChgState( gFaceClr,gFaceClr,0 )
obj.style.posTop=3D0
}
function _IBSetE( state )
{
var t=3Dthis
GetObj( t.mBorderId ).style.visibility=3D"visible"
if( state !=3D t.mIsOn ) {
t.mIsOn=3Dstate
if( state )
t.SetInactive()
else
t.SetDisabled()
}
}
function _IBP()
{
var t=3Dthis
if( t.mIsOn ) {
if( t.UserAction !=3D null )
t.UserAction()
if( t.ChangeIcon ) {
obj=3DGetObj(t.mObjId)
if( t.ChangeIcon() )
obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-4)*t.mWidth
else
obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-0)*t.mWidth
}
t.SetActive()
}
}
function _IBUI( clr1,clr2,nextState )
{
var t=3Dthis
SetBorder( GetObj( t.mBorderId ),clr1,clr2 )
obj=3DGetObj( t.mObjId )
obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-nextState)*t.mWidth-obj=
.style.posTop
t.mCurState=3DnextState
return obj
}
function TxtBtn( oId,oeId,action,chkState )
{
var t=3Dthis
t.Perform =3D _TBP
t.SetActive =3D _TBSetA
t.SetInactive=3D _TBSetI
t.SetPressed =3D _TBSetP
t.SetDisabled=3D _TBSetD
t.SetEnabled =3D _TBSetE
t.GetState =3D chkState
t.UserAction =3D action
t.ChgState =3D _TBUI
t.mObjId =3D oId
t.m_elementsId=3D oeId
t.mIsOn =3D 1
}
function _TBSetA()
{
var t=3Dthis
if( t.mIsOn && !t.GetState() )
t.ChgState( gHiliteClr,gShadowClr,0,0 )
}
function _TBSetI()
{
var t=3Dthis
if( t.mIsOn && !t.GetState() )
t.ChgState( gFaceClr,gFaceClr,0,0 )
}
function _TBSetP()
{
if( this.mIsOn )
this.ChgState( gShadowClr,gHiliteClr,1,1 )
}
function _TBSetD()
{
this.ChgState( gFaceClr,gFaceClr,0,0 )
this.mIsOn =3D 0
}
function _TBSetE()
{
var t=3Dthis
if( !t.GetState() )
t.ChgState( gFaceClr,gFaceClr,0,0 )
else
t.ChgState( gShadowClr,gHiliteClr,1,1 )
t.mIsOn =3D 1
}
function _TBP()
{
var t=3Dthis
if( t.mIsOn ) {
if( t.UserAction !=3D null )
t.UserAction()
if( !t.GetState )
return
if( t.GetState() )
t.SetPressed()
else
t.SetActive()
}
}
function _TBUI( clr1,clr2,lOffset,tOffset )
{
SetBorder( GetObj( this.mObjId ),clr1,clr2 )
Offset( GetObj( this.m_elementsId ),lOffset,tOffset )
}
function Offset( obj, top, left ){ obj.style.top=3Dtop; obj.style.left=3Dle=
ft }
function SetBorder( obj, upperLeft, lowerRight )
{
s=3Dobj.style;
s.borderStyle =3D "solid"
s.borderWidth =3D 1
s.borderLeftColor =3D s.borderTopColor =3D upperLeft
s.borderBottomColor=3D s.borderRightColor =3D lowerRight
}
function GetBtnObj(){ return gBtnArr[window.event.srcElement.id] }
function BtnOnOver(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetActive() }
function BtnOnDown(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetPressed() }
function BtnOnOut(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetInactive() }
function BtnOnUp()
{
b=3DGetBtnObj()
if( b !=3D null )
b.Perform()
else
Upd()
}
function GetNtsState(){ return parent.gNtsOpen }
function GetOtlState(){ return parent.gOtlOpen }
function GetOtlTxtState(){ return parent.gOtlTxtExp }
function NtsBtnSetFlag( fVal )
{
s=3Ddocument.all.item( this.m_flagId ).style
s.display=3D"none"
if( fVal )
s.display=3D""
else
s.display=3D"none"
}
function _BSetA_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S=
etActive() }
function _BSetI_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S=
etInactive() }
function _BSetP_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S=
etPressed() }
function _BSetA_BorderImg()
{
b =3D gBtnArr[this.mBorderId]
if( b !=3D null && this.mIsOn && !b.GetState() ) {
obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 )
obj.style.posTop=3D0
}
}
function _BSetI_BorderImg()
{
b =3D gBtnArr[this.mBorderId]
if( b !=3D null && this.mIsOn && !b.GetState() ) {
obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 )
obj.style.posTop=3D0
}
}
var gHiliteClr=3D"THREEDHIGHLIGHT",gShadowClr=3D"THREEDSHADOW",gFaceClr=3D"=
THREEDFACE"
var gBtnArr =3D new Array()
gBtnArr["nb_otl"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOtlPan=
e,GetOtlState )
gBtnArr["nb_otlElem"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOt=
lPane,GetOtlState )
gBtnArr["nb_nts"] =3D new ImgBtn( "nb_nts","nb_ntsBorder",10,parent.ToggleN=
tsPane )
gBtnArr["nb_nts"].SetActive =3D _BSetA_BorderImg;
gBtnArr["nb_nts"].SetInactive =3D _BSetI_BorderImg;
gBtnArr["nb_ntsBorder"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.=
ToggleNtsPane,GetNtsState )
gBtnArr["nb_ntsElem"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.To=
ggleNtsPane,GetNtsState )
gBtnArr["nb_prevBorder"] =3D gBtnArr["nb_prev"]=3D new ImgBtn( "nb_prev","n=
b_prevBorder",30,parent.GoToPrevSld )
gBtnArr["nb_nextBorder"] =3D gBtnArr["nb_next"]=3D new ImgBtn( "nb_next","n=
b_nextBorder",30,parent.GoToNextSld )
gBtnArr["nb_sldshw"]=3D new ImgBtn( "nb_sldshw","nb_sldshwBorder",18,parent=
.FullScreen )
gBtnArr["nb_sldshwBorder"] =3D new TxtBtn( "nb_sldshw","nb_sldshwBorder",pa=
rent.FullScreen,null )
gBtnArr["nb_sldshwBorder"].SetActive =3D _BSetA_Border;
gBtnArr["nb_sldshwBorder"].SetInactive =3D _BSetI_Border;
gBtnArr["nb_sldshwText"] =3D new TxtBtn( "nb_sldshw","nb_sldshwText",parent=
.FullScreen,null )
gBtnArr["nb_sldshwText"].SetActive =3D _BSetA_Border;
gBtnArr["nb_sldshwText"].SetInactive =3D _BSetI_Border;
gBtnArr["nb_voice"] =3D gBtnArr["nb_voiceBorder"] =3D new ImgBtn( "nb_voice=
","nb_voiceBorder",18,parent.ToggleVNarration )
gBtnArr["nb_otlTxtBorder"] =3D gBtnArr["nb_otlTxt"]=3D new ImgBtn( "nb_otlT=
xt","nb_otlTxtBorder",23,parent.ToggleOtlText )
gBtnArr["nb_ntsBorder"].m_flagId=3D "nb_nts"
gBtnArr["nb_ntsBorder"].SetFlag =3D NtsBtnSetFlag
gBtnArr["nb_otlTxt"].ChangeIcon=3D GetOtlTxtState
var sNext=3D"Next",sPrev=3D"Previous",sEnd=3D"End Show",sFont=3D"Arial",sAr=
row=3D"Arrow",sFreeform=3D"Freeform",sRect=3D"Rectangle",sOval=3D"Oval"
function ShowMenu()
{
BuildMenu();
var doc=3DPPTSld.document.body,x=3DPPTSld.event.clientX+doc.scrollLeft,y=
=3DPPTSld.event.clientY+doc.scrollTop
m =3D PPTSld.document.all.item("ctxtmenu")
m.style.pixelLeft=3Dx
if( (x+m.scrollWidth > doc.clientWidth)&&(x-m.scrollWidth > 0) )
m.style.pixelLeft=3Dx-m.scrollWidth
m.style.pixelTop=3Dy
if( (y+m.scrollHeight > doc.clientHeight)&&(y-m.scrollHeight > 0) )
m.style.pixelTop=3Dy-m.scrollHeight
m.style.display=3D""
}
function _CM()
{
if( !parent.IsFullScrMode() ) return;
if(!PPTSld.event.ctrlKey) {
ShowMenu()
return false
} else
HideMenu()
}
function BuildMenu()
{
if( PPTSld.document.all.item("ctxtmenu") ) return
var mObj=3DCreateItem( PPTSld.document.body )
mObj.id=3D"ctxtmenu"
mObj.style.visibility=3D"hidden"
var s=3DmObj.style
s.position=3D"absolute"
s.cursor=3D"default"
s.width=3D"120px"
SetCMBorder(mObj,"menu","black")
var iObj=3DCreateItem( mObj )
SetCMBorder( iObj, "threedhighlight","threedshadow" )
iObj.style.padding=3D2
CreateMenuItem( iObj,sNext,M_GoNextSld,M_True )
CreateMenuItem( iObj,sPrev,M_GoPrevSld,M_HasPrevSld )
CreateSeparator( iObj )
CreateMenuItem( iObj,sEnd,M_End,M_True )
mObj.style.visibility=3D"visible"
}
function Cancel() { window.event.cancelBubble=3Dtrue; window.event.returnVa=
lue=3Dfalse }
function Highlight() { ChangeClr("activecaption","threedhighlight") }
function Deselect() { ChangeClr("threedface","menutext") }
function Perform()
{
e=3DPPTSld.event.srcElement
if( e.type=3D=3D"menuitem" && e.IsActive() )
e.Action()
else
PPTSld.event.cancelBubble=3Dtrue
}
function ChangeClr( bg,clr )
{
e=3DPPTSld.event.srcElement
if( e.type=3D=3D"menuitem" && e.IsActive() ) {
e.style.backgroundColor=3Dbg
e.style.color=3Dclr
}
}
function M_HasPrevSld() { return( parent.HasPrevSld() ) }
function M_GoNextSld() { if( gIsEndShow ) M_End(); else GoToNextSld() }
function M_GoPrevSld() { if( gIsEndShow ) { gIsEndShow=3D0; history.back();=
PPTSld.event.cancelBubble=3Dtrue; } else GoToPrevSld() }
function M_True() { return true }
function M_End() { window.close( self ) }
function CreateMenuItem( node,text,action,eval )
{
var e=3DCreateItem( node )
e.type=3D"menuitem"
e.Action=3Daction
e.IsActive=3Deval
e.innerHTML=3Dtext
if( !e.IsActive() )
e.style.color=3D"threedshadow"
e.onclick=3DPerform
e.onmouseover=3DHighlight
e.onmouseout=3DDeselect
s=3De.style;
s.fontFamily=3DsFont
s.fontSize=3D"9pt"
s.paddingLeft=3D2
}
function CreateSeparator( node )
{
var sObj=3DCreateItem( node )
SetCMBorder(sObj,"menu","menu")
var s=3DsObj.style
s.borderTopColor=3D"threedshadow"
s.borderBottomColor=3D"threedhighlight"
s.height=3D1
s.fontSize=3D"0px"
}
function CreateItem( node )
{
var elem=3DPPTSld.document.createElement("DIV")
node.insertBefore( elem )
return elem
}
function SetCMBorder( o,ltClr,rbClr )
{
var s=3Do.style
s.backgroundColor=3D"menu"
s.borderStyle=3D"solid"
s.borderWidth=3D1
s.borderColor=3DltClr+" "+rbClr+" "+rbClr+" "+ltClr
}
------=_NextPart_01CA71BE.E4369DF0
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------=_NextPart_01CA71BE.E4369DF0
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------=_NextPart_01CA71BE.E4369DF0
Content-Location: file:///C:/B96BA213/NumberSystems_files/frame.htm
Content-Transfer-Encoding: quoted-printable
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Number Systems
------=_NextPart_01CA71BE.E4369DF0
Content-Location: file:///C:/B96BA213/NumberSystems_files/outline.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
No=
tes
1
2
In every numbering system digits are written in columns. Each column
represents a different value.
In the decimal system the rightmost column represents the
“ones”, the second to last column the “tens”=
the
third to last the “one hundreds”.
3
4
5
6
The hexadecimal system, HEX, uses 16 digits to represent numbers:
0 1 2 3 4 5 6 7 8 9 A B C D E F
For example the number=
7B
represents: 11x1 + 7x16 =3D 123
4 digit binary numbers can represented by one HEX digit. Therefore l=
ong
binary numbers can be easily represented by shorter HEX numbers.
One 16 bit number can be represented by only 4 HEX numbers.
For example: Binary 1011 0000 0111 1100 translates to HEX B07C
11002 =3D 1210 =3D CHEX
01112 =3D 710 =3D 7HEX
00002 =3D 010 =3D 0HEX
10112 =3D 1110 =3D BHEX
7
8
MIDI <=
/div>
MIDI uses a 7 digit binary system to represent the values of most
parameters (program, volume, pan, modulation)
7bits can only represent values from 0 to 127
Two sets of 7 digits can be used for a total of 32768 discrete numbe=
rs
– (Pitch Bend)
MIDI Channel only has four bits for a maximum possible 16 channels=
li>
9
8 bit can represent 256 discrete numbers
12 bit - 4096
16 bit - 65,536
20 bit - 1,048,576
24 bit – 16,777,216
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////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
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