Download - Binary
BinaryBinary
In 1854, British mathematician In 1854, British mathematician George BooleGeorge Boole published a paper published a paper
detailing a system of logic that would detailing a system of logic that would become known as become known as Boolean algebraBoolean algebra..
His logical system proved instrumental His logical system proved instrumental in the development of the binary in the development of the binary
system, particularly in its system, particularly in its implementation in electronic circuitry.implementation in electronic circuitry.
BinaryBinaryA numbering systems that only uses two A numbering systems that only uses two
digits. digits. 00 and and 11..Rather than a base ten that we are all Rather than a base ten that we are all
familiar with.familiar with. Computers use binary to store Computers use binary to store information in a digital format.information in a digital format.
Each digit ( Each digit ( 00 or or 11) represents one bit) represents one bitEight bits are equal to one byte.Eight bits are equal to one byte.
Bit Bit One Binary DigitOne Binary Digit abbreviation is “abbreviation is “bb””
Can be thought of as one characterCan be thought of as one character
Either a Either a 11 or a or a 0 0
ByteByte
Eight Eight bits bits make up make up one byteone byte
Abbreviation “Abbreviation “BB””
Combination of Combination of 1’s1’s and and 0’s0’s
Can be thought of as one characterCan be thought of as one character
1110101011101010
kilobitkilobit1024 1024 bitsbits
Abbreviation “Abbreviation “KbKb””
kilobytes kilobytes
Represented by Represented by KBKB
Slang Slang “Kilo”“Kilo”
Is equal to Is equal to 1024 bytes1024 bytes
221010
megabytesmegabytes
Represented by Represented by MBMB
Slang Slang “Meg”“Meg”
Is equal to Is equal to 1,000000 bytes1,000000 bytes
One million bytesOne million bytes
222020
gigabytegigabyte
Represented by GBRepresented by GB
Slang Slang “Gig”“Gig”
Equal to Equal to 1,000,000,000 Bytes1,000,000,000 Bytes
One Billion bytesOne Billion bytes
2230 30
terabyteterabyte
Represented by TBRepresented by TB
Slang Slang “tera”“tera”
Equal to Equal to 1,000,000,000,000 Bytes1,000,000,000,000 Bytes
One Trillion bytesOne Trillion bytes
224040
petabytepetabyte
Represented by PBRepresented by PB
Slang Slang “peta”“peta”
Equal to Equal to 1,000,000,000,000,000 1,000,000,000,000,000 BytesBytes
One Thousand Trillion bytesOne Thousand Trillion bytes
225050
exabyteexabyteRepresented by EBRepresented by EBSlang Slang “exa”“exa”Equal to Equal to 1,000,000,000,000,000,000 1,000,000,000,000,000,000 BytesBytes One Million Trillion bytesOne Million Trillion bytes226060
All printed materialin the worldAll printed materialin the world would use about 5 would use about 5 ExabytesExabytes
Binary Binary
Think of Binary as light bulbs Think of Binary as light bulbs
that are either ON that are either ON or Offor Off
Binary Binary
One Light bulb represents one One Light bulb represents one BitBit
All All eight eight of these Light bulbs of these Light bulbs would represent one byte would represent one byte
Binary Binary
Think of Binary as light bulbs Think of Binary as light bulbs
that are either ON that are either ON or Offor Off
11 00 00 00 00 00 00 11
Binary ExerciseBinary Exercise
Bit Postion Bit 8 Bit 7 Bit 6 Bit 5 Bit 4 Bit 3 Bit 2 Bit 1 Total Binary ValuePosition Value
if ON128 64 32 16 8 4 2 1 255
Position Valueif OFF
0 0 0 0 0 0 0 0 0
Turn a Postion ON
1 0 0 0 0 0 0 1
Here we would ADD
The Postion Value
Here we bringThe Postion
Value DOWN
128 1 129
In this incidence our binary Number 10000001 would have a value of 129Because Postion 8 is ON Postion 7 is OFF Postion 6 is OFF Position 5 is OFF Position 4 is Off
Postion 3 is OFF Postion 2 is OFF and Position 1 is ON.
Binary Exercise
BinaryBinary
Figuring Binary.Figuring Binary.Starting on the right going to the leftStarting on the right going to the leftThe The first digit will be digit will be 1 1The The secondsecond digit will be digit will be 2 2The The thirdthird digit will be digit will be 4 4The The fourthfourth digit will be digit will be 8 8The The fifthfifth digit will be digit will be 16 16The The sixth sixth digit will be digit will be 32 32The The seventhseventh digit will be digit will be 64 64The The eightheighth digit will be digit will be 128128
Binary Binary
Base Ten numbers are tabulatedBase Ten numbers are tabulated
Left to Right.Left to Right.
Binary Binary
Binary numbers are tabulatedBinary numbers are tabulated
Right to Left.Right to Left.
Example10000000
The 1st – 7th digit would be OffThe Eighth digit would be On
The first digit will be 1 0The second digit will be 2 0The third digit will be 4 0The fourth digit will be 8 0The fifth digit will be 16 0The sixth digit will be 32 0The seventh digit will be 64 0The eighth digit will be 128 ++128128
Add the bitsAdd the bits
The value of the number would be Total 128128
Example10000001
The 1st digit would be OnThe 2nd – 7th digit would be OffThe Eighth digit would be On
The first digit will be 1 1The second digit will be 2 0The third digit will be 4 0The fourth digit will be 8 0The fifth digit will be 16 0The sixth digit will be 32 0The seventh digit will be 64 0The eighth digit will be 128 ++128128
Add the bitsAdd the bits
The value of the number would be Total 129129
Example10000011
The 1st digit would be OnThe 2nd digit would be OnThe 3rd – 7th digit would be OffThe Eighth digit would be On
The first digit will be 1 1The second digit will be 2 2The third digit will be 4 0The fourth digit will be 8 0The fifth digit will be 16 0The sixth digit will be 32 0The seventh digit will be 64 0The eighth digit will be 128 ++128128
Add the bitsAdd the bits The value of the number would be Total 131131
Example10000111
The 1st- 3rd digit would be OnThe 4th – 7th digit would be OffThe Eighth digit would be On
The first digit will be 1 1The second digit will be 2 2The third digit will be 4 4The fourth digit will be 8 0The fifth digit will be 16 0The sixth digit will be 32 0The seventh digit will be 64 0The eighth digit will be 128 ++128128
Add the bitsAdd the bits
The value of the number would be Total 135135
Example11000000
The 1st- 6th digit would be OffThe 7th digit would be OnThe 8th digit would be On
The first digit will be 1 0The second digit will be 2 0The third digit will be 4 0The fourth digit will be 8 0The fifth digit will be 16 0The sixth digit will be 32 0The seventh digit will be 64 64The eighth digit will be 128 ++128128
Add the bitsAdd the bits
The value of the number would be Total 192192
Binary Binary
Think of Binary as light bulbs Think of Binary as light bulbs
that are either ON that are either ON or Offor Off
11 11 00 00 00 00 00 00
What is the What is the value?value?
192192
Example11111111
The 1st- 8th digit would be On
The first digit will be 1 1The second digit will be 2 2The third digit will be 4 4The fourth digit will be 8 8The fifth digit will be 16 16The sixth digit will be 32 32The seventh digit will be 64 64The eighth digit will be 128 ++128128
Add the bitsAdd the bits
The value of the number would be Total 255255 11 11 00 00 00 00 00 00
Binary Binary
Think of Binary as light bulbs Think of Binary as light bulbs
that are either ON that are either ON or Offor Off
11 11 11 11 11 11 11 11
What is the What is the value?value?
255255
128128 6464 3232 1616 88 44 22 11
Using CalculatorUsing Calculatorto figureto figure
Binary NumbersBinary Numbers
First we would open First we would open CalculatorCalculator Start/All Programs/Accessories/Start/All Programs/Accessories/CalculatorCalculator
From the Calculator go to View and down From the Calculator go to View and down
To SCIENTIFICTo SCIENTIFIC
Scientific
This is the Scientific Calculator This is the Scientific Calculator
The next thing we would need to do The next thing we would need to do in select in select – BINBIN for Binary for Binary
Next we would enter the Binary Next we would enter the Binary numbernumber
For exampleFor example
1000000010000000
After entering the Binary number we After entering the Binary number we would then select the would then select the
DecDec Radio Button Radio Button
We now see the answer to the problemWe now see the answer to the problem
Is Is
128128
Binary Binary
Think of Binary as light bulbs Think of Binary as light bulbs
that are either ON that are either ON or Offor Off
11 11 00 00 00 00 00 00
What is the What is the value?value?
192192