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



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




Example10000011

The 1st digit would be OnThe 2nd digit would be OnThe 3rd – 7th digit would be OffThe Eighth digit would be On


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




Example11000000

The 1st- 6th digit would be OffThe 7th digit would be OnThe 8th digit would be On




Binary Binary



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 value of the number would be Total 255255 11 11 00 00 00 00 00 00

Binary Binary



11 11 11 11 11 11 11 11


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



11 11 00 00 00 00 00 00


192192

Technology

Binary