Binaryconversion 090715011937-phpapp01

Binary
In 1854, British mathematicianIn 1854, British mathematician
George BooleGeorge Boole published a paperpublished a paper
detailing a system of logic that woulddetailing a system of logic that would
become known asbecome known as Boolean algebraBoolean algebra..
His logical system proved instrumentalHis logical system proved instrumental
in the development of the binaryin the development of the binary
system, particularly in itssystem, particularly in its
implementation in electronic circuitry.implementation in electronic circuitry.

Binary
A numbering systems that only usesA numbering systems that only uses
two digits.two digits. 00 andand 11..
Rather than a base ten that we are allRather than a base ten that we are all
familiar with.familiar with.
Computers use binary to storeComputers use binary to store
information in a digital format.information in a digital format.
Each digit (Each digit ( 00 oror 11) represents one bit) represents one bit
Eight bits are equal to one byte.Eight bits are equal to one byte.

Bit
 One Binary Digit
 abbreviation is “b”
Can be thought of as one character
 Either a 1 or a 0

Byte
 Eight bits make up one byte
 Abbreviation “B”
 Combination of 1’s and 0’s
 Can be thought of as one character
11101010

kilobit
1024 bits
 Abbreviation “Kb”

kilobytes
 Represented by KB
 Slang “Kilo”
 Is equal to 1024 bytes
 210

megabytes
 Represented by MB
 Slang “Meg”
 Is equal to 1,000000 bytes
 One million bytes
 220

gigabyte
 Represented by GB
 Slang “Gig”
 Equal to 1,000,000,000 Bytes
 One Billion bytes
 230

terabyte
 Represented by TB
 Slang “tera”
 Equal to 1,000,000,000,000 Bytes
 One Trillion bytes
 240

petabyte
 Represented by PB
 Slang “peta”
 Equal to 1,000,000,000,000,000 Bytes
 One Thousand Trillion bytes
 250

exabyte
 Represented by EB
 Slang “exa”
 Equal to 1,000,000,000,000,000,000 Bytes
 One Million Trillion bytes
 260
 Allprintedmaterialintheworld
would use about 5 Exabytes

Think of Binary as light bulbs
that are either ON
or Off

All eight of these Light bulbs would represent one byte
One Light bulb represents oneOne Light bulb represents one
BitBit

that are either ON
or Off
11 00 00 00 00 00 00 1111 00

Binary ExerciseBinary Exercise
Bit Postion Bit 8 Bit 7 Bit 6 Bit 5 Bit 4 Bit 3 Bit 2 Bit 1 Total Binary Value
Position Value
if ON
128 64 32 16 8 4 2 1 255
Position Value
if 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 bring
The Postion
Value
DOWN
128 1 129
In this incidence our binary Number 10000001 would have a value of 129
Because 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

Binary
 Figuring Binary.
 Starting on the right going to the left
 The first digit will be 1
 The second digit will be 2
 The third digit will be 4
 The fourth digit will be 8
 The fifth digit will be 16
 The sixth digit will be 32
 The seventh digit will be 64
 The eighth digit will be 128

Binary
Base Ten numbers are tabulated
Left to Right.

Binary
Binary numbers are tabulated
Right to Left.

Example
10000000
The 1st
– 7th
digit would be Off
The Eighth digit would be On
 The first digit will be 1 0
 The second digit will be 2 0
 The third digit will be 4 0
 The fourth digit will be 8 0
 The fifth digit will be 16 0
 The sixth digit will be 32 0
 The seventh digit will be 64 0
 The eighth digit will be 128 +128
Add the bits
The value of the number would be Total 128

Example
10000001
The 1st
digit would be On
The 2nd
– 7th
digit would be Off
Add the bits

Example
10000011
The 1st
digit would be On
The 2nd
digit would be On
The 3rd
– 7th
digit would be Off
Add the bits

Example
10000111
The 1st-
3rd
digit would be On
The 4th
– 7th
digit would be Off
Add the bits

Example
11000000
The 1st-
6th
digit would be Off
The 7th
digit would be On
The 8th
digit would be On
Add the bits

that are either ON
or Off
11 11 00 00 00 00 00 00
What is theWhat is the
value?value?
192192

Example
11111111
The 1st-
8th
digit would be On
Add the bits

that are either ON
or Off
11 11 11 11 11 11 11 11
What is theWhat is the
value?value?
255255
128128 6464 3232 1616 88 44 22 11

Using Calculator
to figure
Binary Numbers
First we would open Calculator
Start/All Programs/Accessories/Calculator
From the Calculator go to View and down
To SCIENTIFIC

Binaryconversion 090715011937-phpapp01

 This is the Scientific Calculator
 The next thing we would need to do in select
 BIN for Binary

 Next we would enter the Binary number
 For example
10000000

After entering the Binary number we would
then select the
Dec Radio Button

We now see the answer to the problem
Is
128

Decimal to Binary
 It follows a starightforward method.
 It involves dividing the number to be
converted, say N by 2 (since binary is in base
2) until we reach the division of (1/2), also
making note of all remainders.

Example 1: Convert 98 from
decimal to binary
 Divide 98 by 2, make note of all the
remainder.
 Continue dividingquotientsby 2, making
notes of the remainder.
 Also, note the star beside the last remainder.

Division Remainder, R
98/2 = 49 R=0
49/2 = 24 R=1
24/2 = 12 R=0
12/2 = 6 R=0
6/2 = 3 R=0
3/2 = 1 R=1
1/2 = 0 R=1
The sequance of remainders going up gives the answer.
Starting from 1*, we have 1100010.
Therefore, 98 in decimals is 1100010 in binary

Example 2: Convert 21 into
binary
Division Remainder, R
21/2 = 10 R=1
10/2 = 5 R=0
5/2 = 2 R=1
2/2 = 1 R=0
1/2 = 0 R=1
Therefore, 21 in decimals is 10101 in binary

Binary to decimal
 Conversion follows the same steps as decimal
to binary, except in reverse order.
 We can begin by multiplying 0 x 2 and adding
1.
 We continue to multiply the numbers in the
“results” column by 2, and adding the digits
from left to right in our binary numbers.

Example 1: Convert 11101
from binary to decimal
Operations Result
0 x 2 + 1 1
1 x 2 + 1 3
3 x 2 + 1 7
7 x 2 + 0 14
14 x 2 + 1 29
Therefore, 11101 in binary is 29 in decimal.

Binaryconversion 090715011937-phpapp01

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