#1**+5 **

HEX means hexadecimal system which includes 0-9, A-F.

Conversion is done in the similar manner we convert to binary

Guest Feb 17, 2015

#2**+5 **

**HEX stands for Hexidecimal.** **Which is base 16**

Hex means 6 and decimal means 10 so Hexidecimal refers to 16

Normally our numbers are in base 10

We need 10 different digits to express our numbers. that is 0,1,2,3,4,5,6,7,8, and 9

so the base 10 number $$36742 = 3*10^4\;\;+\;\;6*10^3\;\;+\;\;7*10^2\;\;+\;\;4*10^1\;\;+\;\;2*10^0$$

Computers actually work in binary. That is base 2. Each individual signal is either on or off. 0 or 1

So the number

$$\\10011010_2 = 1*2^7\;\;+\;\;1*2^4\;\;+\;\;1*2^3\;\;+\;\;1*2^1 \\\\

= 128+16+8+2=154_{10}\;\;$That means 154 base 10$$$

Now to write everynumber out in base 2 would take for ever. So computer geeks change it to base 16 which is hexidecimal.

For base 16, 16 digits are needed, they are 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

Now I will try and show you why this is useful. You need to recognise that $$16=2^4$$

Lets look at our base 2 number

$$\\10011010_2$$ I am going to seperate this into groups of 4 like this

$$\\\underbrace{1001}\underbrace{1010}\; base \;2\\\\

now\: 1001_2 = 8+1=9\; $ base 10, and that is also 9 in base 16 \\

and\; 1010_2 = 8+2=10\; $ base 10, and that is A in base 16 \\

so\\

\mbox {10011010 is 9A as a hexidecimal number}$$

Lets just check this. We already discovered that 10011010 base two = 154 base 10

Lets see what 9A base 16 is in base 10

$$\\9A\; (base 16)= 9*16^1+10 = 144+10 = 154\;\;(base 10)\\\\

\mbox{so it has been established that}\\\\

154_{10}=10011010_2=9A_{16}$$

I DO HOPE SOMEONE GETS SOMETHING OUT OF THIS POST BECAUSE IT HAS TAKEN AGES TO WRITE IT.

(I have had lots of interuptions)

Melody
Feb 18, 2015