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Hexidecimal Tutorial

Started by screamingman12, August 22, 2007, 01:02:58 PM

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screamingman12

I have been taking the Cisco Networking classes at school, as part of that, I learned Hexidecimal. After reading the tutorial on ST,I have found the Cisco way to be much easier. 

For those who don't already know:

Hexidecimal= Base 16 (0-F)
Decimal= Base 10 (0-9)
Binary= Base 2 (0-1)

Start with this table, this tells you the binary equivalent for each hexidecimal number:

Hexidecimal  Binary   Decimal
0                    0000         0
1                    0001         1 
2                    0010         2
3                    0011         3
4                    0100         4
5                    0101         5
6                    0110         6
7                    0111         7
8                    1000         8
9                    1001         9
A                    1010         10
B                    1011         11
C                    1100         12
D                    1101         13
E                    1110         14
F                    1111         15

convert with this (note: numbers in parentheses represent superscripts)

2(11) 2(10) 2(9) 2(8 ) | 2(7) 2(6) 2(5) 2(4) | 2(3) 2(2) 2(1) 2(0)
2048  1024  512  256 |  128  64   32   16   |  8     4       2    1


so for example '4AF' in hex would be 0100 | 1010 | 1111 in binary (see first chart), plug that into the chart:

2(11) 2(10) 2(9) 2(8 ) | 2(7) 2(6) 2(5) 2(4) | 2(3) 2(2) 2(1) 2(0)
2048  1024  512  256 |  128  64   32   16   |  8     4       2    1
   0       1       0    0  |    1     0     1     0  |  1      1       1    1

Then, add all the numbers with a 1 underneath them:

1024+128+32+8+4+2+1= 1199 in decimal

going from decimal to hex:

let's make 744 a hexidecimal number:

find the largest number on the chart you can subtract 744 from without having a negative number, that's 512:

744-512= 232

so put a 1 under 512

2(11) 2(10) 2(9) 2(8 ) | 2(7) 2(6) 2(5) 2(4) | 2(3) 2(2) 2(1) 2(0)
2048  1024  512  256 |  128  64   32   16   |  8     4       2    1
0       0       1     


and so on:

232-128= 104

2(11) 2(10) 2(9) 2(8 ) | 2(7) 2(6) 2(5) 2(4) | 2(3) 2(2) 2(1) 2(0)
2048  1024  512  256 |  128  64   32   16   |  8     4       2    1
0         0      1      0       1

104-64=40


40-32=8

2(11) 2(10) 2(9) 2(8 ) | 2(7) 2(6) 2(5) 2(4) | 2(3) 2(2) 2(1) 2(0)
2048  1024  512  256  |  128  64   32   16   |  8     4       2    1
0         0      1      0  |    1     1     1    0   |    1     0       0    0

so 744 in decimal is 001011101000 in binary, or 2E8 in hex.

Hope this helps.














"...the streetcar, the carriage of the people, was opposed; but that which is for the greatest good of the greatest number will always conquer in the end..." -Rapid Transit in Cities, Thomas Curtis Clarke, 1892

RippleJet

#1
Screamingman12, you made a mistake in the dec->hex conversion, due to the fact that you've entered 28 to be 156 instead of 256.

The fastest way to convert between HEX/DEC/OCT/BIN is to use the Windows Calculator (in advanced mode).

You can quickly switch between those four bases by pressing F5...F8:

     F5 = Hexadecimal
     F6 = Decimal
     F7 = Octal
     F8 = Binary

If you start the Calculator, press F6, enter 744 (decimal), and then press F5 and F8, you will see that 74410 = 2E816 = 0010 1110 10002

screamingman12

RippleJet, I fixed the tutorial, it should be okay.

and yes, I will admit that the quickest way to do it is the windows calculator, but this is still pretty easy.


"...the streetcar, the carriage of the people, was opposed; but that which is for the greatest good of the greatest number will always conquer in the end..." -Rapid Transit in Cities, Thomas Curtis Clarke, 1892