Intoduction.txt

//////////////// Number System /////////////////////

1. What is Number System ?
Sol : 
Console it 0.1 + 0.2 = 0.3000000000000004

If your System didn't  understand the encoded part ...your data will be corrupted
Because of the losing bits

Even if you use recovery software ...your data will be not in same quality as it was before
because they lost bits ...lost in bits ..lost in data ...lots in kb...lost in clarity

The DPI bits in Ratio .......
Density Per Ratio

If you see the text in boxes then your data is corrupted

why 1 emotion is taking length as 2 (👋 = length = 2)
and 1 character is taking length as 1 ( (a = 2) = a.length = 1)

ASCCI is a Subset of UTF


Unicode Transformation Format (UTF)
Common Code points = UTF-8,UTF-


 UTF has 0 -7424 characters 
 This defines a UTF-16 Table, which uses 16-bits to define the characters.
  | 
ASCCI has 0 - 127 characters


Make Web Apps Which Supports and Uses UTF-16 Table
It Make Sures that data is not lost and not corrupted
Sender and Receiver Should be in Sync Both Should be accpeting the UTF-16 Table

Add Meta Tag <meta charset = "utf-16"> to both Should be in Sync 



Number Systems : Its All about to represent a particular value
(Number of digits you have to represent it)
A numeral system is a writing system for expressing numbers;
that is, a mathematical notation for representing numbers of
a given set, using digits or other symbols in a consistent manner.
The same sequence of symbols may represent different numbers in different numeral systems

We Human use Decimal numbers

Types Of Number System
1. Decimal Number (0-9) (10 is the Radix / Base ) // Because 10 digits are there in 0 to 9 
2. Binary Number (0-1) (2 is the Radix / Base ) // Because 2 digits are there in 0 to 1
3. Octal Number (0-7) (8 is the Radix / Base ) // Because 8 digits are there in 0 to 7



55$ Apple Product 

How 55 become in Decimal is where radix is in 10 because its Decimal radix is 10

5      5 
x       x
10^1 + 10^0 
10^1 = 10 and 10 X 5 = 50 ; 10^0 = 1 and 1 x 5 = 5 ; and 50 + 5 is 55

50   + 5 = 55


324 Radix is 10


3    2    4
10^2 10^1 10^0 

300 + 20 + 4 = 324
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(Binary to Decimal) 
1   0   1   1    0 
2^4+2^3+2^2+2^1+2^0
= 22
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Terenry to Decimal

2   1      0
3^2 + 3^1 + 3^0 
9+3+= 11
There are 4 Types of Number Systems we have
Decimal Number System
Binary Number System
Octal Number System
Hexadecimal Number System
Radix / Base: Number of Digits you have in a Number System

Decimal Number System
Decimal comes from the Latin word Decimus, meaning tenth, from the root word decem, or 10. The decimal system,
therefore, has 10 as its base /Radix and is sometimes called a base-10 system. … The decimal point, for example,
refers to the period that separates the ones place from the tenths place in decimal numbers.
Range : [0,1,2,3,4,5,6,7,8,9]
Example 1 : (14)base10 , (30)base10
How we Define it 5 and 55
Example 1:
Where we know that base is 10 here
base is 10 . So it should be 10 in Multiple
55 = [10(power)0 X 5]+ [10(power)1 X 5]
55 = 5+50
Example 2:
345
300 + 40 + 5
345 = [10(power)2 X 3]+ [10(power)1 X 4]+[10(power)0 X 5]
Same for All Number Systems with respect to their base numbers



Binary Number System
A binary number is a number expressed in the base-2 numeral system or binary numeral system, 
a method of mathematical expression that uses only two symbols: typically “0” and “1”. 
The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred 
to as a bit or binary digit.
Range : [0,1]
Example : (10)base2 , (01)base2



Octal Number System
The octal numeral system, or oct for short, is the base-8 number system and uses the digits 0 to 7, 
that is to say, 10 represents 8 in decimal and 100 represents 64 in decimal
Range :[0,1,2,3,4,5,6,7]
Example : (45)base8 , (34)base8


Hexadecimal Number System
Range :[0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F]
Where
A = 11
B = 12
C = 13
D = 14
E = 15
F = 16
Example : (4A)base16 , (F3)base16



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1.1 Decimal to Binary
(45)₁₀ to ( )₂
1st Method LCM
45/2 Quotient = 22 , Remainder = 1
22/2 Quotient = 11, Remainder = 0
11/2 Quotient = 5 , Remainder = 1
5/2 Quotient = 2, Remainder = 1
2/2 Quotient = 1, Remainder = 0
Take From Last Quotient to Upper Last Remainder
1 0 1 1 0 1
(45)₁₀ = (101101)₂


1.2 Decimal to Octal

(45)₁₀ to ( )₈
2 Methods
Decimal to Octal
Decimal to Binary — Binary to Octal
Decimal to Octal
(45)₁₀ to ( )₈
1st Method LCM
45/8 Quotient = 5, Remainder = 5
5/8 Quotient = 5 , Remainder = 0
5 5
(45)₁₀ to (55 )₈


2nd Method
Decimal to Binary — Binary to Octal
(46)₁₀ to ( )₂
46/2 Quotient = 23 , Remainder = 0
23/2 Quotient = 11, Remainder = 1
11/2 Quotient = 5 , Remainder = 1
5/2 Quotient = 2, Remainder = 1
2/2 Quotient = 1, Remainder = 0
1 0 1 1 1 0
(46)₁₀ = (101110)₂
Binary to Octal
1 0 1 1 1 0
Divide the Number in 2 Parts
101 and 110
1 0 1
²²x1+²¹x0+²⁰x1
4x1+ 2x0 + 1x1
4+1 = 5 (1st Digit) — — — — — — 1
110
²²x1 + ²¹x1 + ²⁰x0
4x1 + 2x1+1x0
4+2 = 6 (2nd Digit) — — — — — — 2
= 56
(101110)₂ = (56)₈

1.3 Decimal to Hexadecimal

(47)₁₀ to ( )₁₆
2 Methods
Decimal to Hexadecimal
Decimal to Binary — Binary to Hexadecimal
1st Method LCM
(47)₁₀ to ( )₁₆
47/16 Quotient = 32, Remainder = 15
32/16 Quotient = 2, Remainder = 0
Where in Hexadecimal F = 15
So There is 2 and F
(47)₁₀ to (2F )₁₆

2nd Method Decimal to Binary — Binary to Hexadecimal
(47)₁₀ to ( )₂
47/2 Quotient = 23 , Remainder = 1
23/2 Quotient = 11, Remainder = 1
11/2 Quotient = 5 , Remainder = 1
5/2 Quotient = 2, Remainder = 1
2/2 Quotient = 1, Remainder = 0
1 0 1 1 1 1
(47)₁₀ to (101111 )₂
Binary to Hexadecimal
1 0 1 1 1 1
Where 1 0 in binary is 2
and 1111 is F
(101111 )₂ = (2F )₁₆

1.4 Decimal to N Base Number
(47)₁₀ to ( )₆
1st Method LCM
47/6 Quotient = 7, Remainder = 5
7/6 Quotient = 1 , Remainder = 1
(47)₁₀= (115)₆