Friday, August 9, 2013

== Learning Hexadecimal ==

   Previously we learned to count in binary which is a base 2 system and is used in computers. There are other base systems that the binary system is usually paired with in computers and that is the base 16 system. In hexadecimal there are 16 different digits usable that being 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. the values are 0 to 15 and like in binary and decimal once you go past that you increment and restart the sequence.

Take a look at this:

Decimal Hexadecimal
0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
10 A
11 B
12 C
13 D
14 E
15 F

    Lets take the same number as last lesson on binary 3,791 as an example. In hexadecimal that value is ECF. To get a better understanding why the value is what it is, lets convert it to binary. Each digit in hexadecimal can be represented with 4 bits like so:

Binary Hexadecimal
0000 0
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
1000 8
1001 9
1010 A
1011 B
1100 C
1101 D
1110 E
1111 F

So in turn the number ECF in binary is:

E C F
1110 1100 1111

As you can see it is identical to the previous lesson, the result being 111011001111. You can also use the place value method as well similar to the binary and decimal system but again the place values are different. You again start with 1 and  each number afterward is a power of 16.

256 16 1
E C F
So using the place value method we do (Ex256) + (Cx16) + (Fx1). You can convert the letters to their respective values if that helps like so : (14x256) + (12x16) + (15x1) = 3,791.

More information can be obtained here : http://en.wikipedia.org/wiki/Hexadecimal

== Learning Binary ==

Binary is a numeric system that uses the base 2 numeral system. There are only 2 usable digits 0 (or off) and 1 (or on). Binary is the heart of all electronic computers, including but not limited to personal computers, Macs, gaming controls, and cellphones. In computers the only thing it really does is switch between 2 states 0 or 1, from that many combinations we get our digital world as we have it today. In this portion I will be showing how to count in binary.
Take a look at the following:
DecimalBinary
00
11
210
311
4100
5101
6110
7111
81000
91001
101010
111011
121100
131101
141110
151111
1610000
1710001
1810010
1910011
2010100

Do you see the pattern?
   In the decimal system we start with 0, and there are 10 usable digits, 0-9. In binary like mentioned there are only 2 digits 0 and 1. In decimal once you get past 9 you simply increment the first digit to the left (if it doesn't exist then pretend its a 0) and start the sequence over. For example: 00,01,02,03,04,05,06,07,08,09 from here we increment to the next digit and start the sequence over again hence we get 10,11,12,13,14, etc.

 In binary its the same concept. 00,01 since 1 is our last usable digit we increment and start the sequence over hence 10,11 from here we repeat the same idea hence 100,101,110,111, etc. Now 100 shown here isn't actually 100 like we use in decimal its value is actually 4. Each place value is different, lets compare it to decimal system:

Note: the value 3,791 is randomly used in this comparison.
Decimal:
1000 100 10 1
3 7 9 1
Binary:
2048 1024 512 256 128 64 32 16 8 4 2 1
1 1 1 0 1 1 0 0 1 1 1 1
   In the decimal system you multiply the number of its place value, and then add the result of each multiplication. So you take (3x1,000) + (7x100) + (9x10) + (1x1) = 3,791.

   In binary it is the same process, just that the place values are different, and easy way to remember is it starts with 1 and is doubled each time. So (1x2,048) + (1x1,024) + (1x512) + (0x256) + (1x128) + (1x64) + (0x32) + (0x16) + (1x8) + (1x4) + (1x2) + (1x1) = 3,791. An obvious way to make this faster is ignore the multiplication part because if its 0 it doesn't add to the value and you can ignore it, and if its 1 just add the place value its because anything multiplied by 1 is equal to itself.

Here is a simple converter:

More information can be obtained here : http://en.wikipedia.org/wiki/Binary_number
 
 
By the end of this lesson you will see there are 10 kind of people in this world those who know binary and those who don't.

Thursday, August 8, 2013

[Computer related tutorials]

In this portion I will be making tutorials and help guides for computer related things that I know/learned to help/teach others, I believe knowledge is power and knowledge should be free

::Content::
Learn Binary
Learn Hexadecimal
Learn Any Base Numbering System