Hexadecimal is the numerical system that most hacking platforms work in. Therefore, it is very useful to have a basic understanding of hex, as it is commonly called.-Hexadecimal?The system we use in our everyday lives is called the decimal system. Its digits are from 0 to 9. In the hexadecimal system, the digits go from 0 to F. There are ten digits (counting 0) in the decimal system: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. In hexadecimal, there are 16 (counting 0): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. You can see that A represents 10, and, by counting, that F represents 15.-Can I have a complete hexadecimal/decimal conversion chart?No. Heheh. In order for me to make one, I would have to type in 65,535 different combinations and their decimal equivalents, and that's only to FFFF. I will, however, give you a chart which should, if you pay attention, easily suffice; hexadecimal on the left, decimal on the right. 0=0 1=1 2=2 3=3 4=4 5=5 6=6 7=7 8=8 9=9 A=10 B=11 C=12 D=13 E=14 F=15 10=16 11=17 12=18 13=19 14=20 15=21 16=22 17=23 18=24 19=25 1A=26 1B=27 1C=28 1D=29 1E=30 1F=31 20=32 30=48 40=64 50=80 60=96 70=112 80=128 90=144 A0=160 B0=176 C0=192 D0=208 E0=224 F0=240 100=256 200=512 300=768 400=1024 500=1280 600=1536 700=1792 800=2048 900=2304 A00=2506 B00=2816 C00=3072 D00=3328 E00=3584 F00=3840 1000=4096 2000=8192 3000=12288 4000=16384 5000=20480 6000=24576 7000=28672 8000=32768 9000=36864 A000=40960 B000=45056 C000=49152 D000=53248 E000=57344 F000=61440 Now let's look at some combinations of high hexadecimal numbers... AA00=43466 AAA0=43626 AAAA=43636 BB00=47872 BBB0=48048 BBBB=48059 CC00=52224 CCC0=52416 CCCC=52428 DD00=56576 DDD0=56784 DDDD=56797 EE00=60928 EEE0=61152 EEEE=61166 FF00=65280 FFF0=65520 FFFF=65535 You will use this chart further on in this FAQ, so take a good look at it and make sure you at least have a basic understanding of it.-Are there any basic rules in hex?There are quite a few, as in any numbering system. I will explain only two which I have found useful here. First, any decimal (our system, as I've said) number that is divisible by 16 (meaning it can be divided by 16 and come out with a whole number) can be easily converted to hex. Simply divide that number by 16, then multiply by 10. Here is an example: I have 64, and want to know what 64 is in hexadecimal. 64 divided by 16 = 4 4 X 10 = 40 64 in hex is 40. Understand? Hopefully, because I'm moving on to another one, heheh. If you want to add a zero to a number in hexadecimal, for example 10 hex, making it (in this example) 100 hex, and determine its new decimal equivalent (assuming, of course, you know the decimal equivalent of the original number), you DO NOT multiply the decimal equivalent by ten, as in our system. The reason you multiply by ten in our system is that in our system, there are ten individual digits, 0-9. In hex, there are 16, 0-F, therefore you must multiply by 16. 16 X 16 = 256 Therefore, 100 hex = 256 dec Here's another example: 3B = 59 3B0 = ? To find the decimal equivalent of 3B0, you must multiply the decimal equivalent of 3B by 16. 59 X 16 = 944 Therefore, the decimal equivalent of 3B0 is 944.-How do I add in hex?To add in hex, simply add in hex, heheh. Here's an example: B + 7 = 12 Look at the chart. This is because B = 11 in decimal, and 7 obviously = 7 in decimal, and 11 + 7 = 18, which in hex is 12. Here's another example: 5 + 4 = 9 This is simple math; nothing is any different here than what the teacher taught you in kindergarten.-How do I add larger numbers in hex?There are two ways I know of (that are feasible) to manually add in hex with large numbers. There are, I'm sure, a few others, but they are far too complicated to ever have any desire to use, especially when you'll get the same answer using these. Say our numbers are 35B and 64C, and we wish to add them together. Here are the two ways we could do that:-The hard wayUsing this method, you will first find the decimal equivalent of each hexadecimal number (use your chart), in this case the decimal equivalent of 35B and 64C. To do this, start by finding the decimal equivalent of the first digit of the first number. In this example,the first number is 35B, and the first digit of it is 300. 300 in decimal = 768 Next, find the equivalent of the second digit, 50. 50 in decimal = 80 Finally, find the equivalent of the last digit, B. B in decimal = 11 Now, add them all (the equivalents) up. 768 + 80 + 11 = 859 Therefore, 35B hex = 859 decimal. Next, move on to the second number, 64C. Start with the first digit, as always. 600 in decimal = 1536 Next, as always, the second digit. 40 in decimal = 64 Finally as always, the last digit. C in decimal = 12 Now (as always, heh), add all the equivalents together. 1536 + 64 + 12 = 1612 Now add both sums together. 859 + 1612 = 2471 Now you must find the hexadecimal equivalent of 2471. The easiest way to go about doing this is to use the chart. You know that 900 in hex = 2304, which is lower than 2471. And A00 in hex = 2506, which is higher than 2471. Therefore, the hex equivalent of 2471 is somewhere between 900 and A00. Now, find the difference between 2471 and the number below it that is the closest number to it that you know of; in this case 2304 (from 900). 2471 - 2304 = 167 167 in hex = A7 (use your chart and some simple addition) Now add A7 to the hex version of the number below 2471 (2304), which is 900. 900 + A7 = 9A7 And there's your answer. 35B + 64C = 9A7-The easy waySimply break down each number by digit, staying in hex for the entire problem, 35B on the left, 64C on the right, and add the individual digits together as I have done below. 300 + 600 = 900 50 + 40 = 90 B + C = 17 Then add the three sums together. 900 + 90 + 17 = 9A7 If you do not see why, look at your chart, and I'll explain as best I can. 900 + 90 = 990 90 + 17 = A7 900 + A7 = 9A7-Is there a basic formula for conversion, so that I might understand why _ in hex = _ in dec?Yes, actually, there is, as there must be for it to be a real numbering system coexisting parallel to decimal. I discovered, while studying binary numbers and their conversion to decimal counterparts, that the same system of equations, representing place values and the numerals occupying them, that is used to convert binary to decimal, would work with not only conversion between any other numbering systems, but also, and obviously, with any numbering system by itself. Here is a quick explanation, in decimal: The decimal number 1234 represents not only a finite number of theoretical objects (discounting a host of other possibilities of its representation), but it also represents an equation. It is as follows (^ represents exponentiation, as in "Squared, to the third power", etc, and remember that any number to the 0th power is 1): 1234 = (1 x 10^3) + (2 x 10^2) + (3 x 10^1) + (4 x 10^0) = (1000) + (200) + (30) + (4) = 1234 Here's another example: 567 = (5 x 10^2) + (6 x 10^1) + (7 x 10^0) = (500) + (60) + (7) = 567 The reason that the number is multiplied by an increasing power of ten is that decimal is ten-base. Were it sixteen-base, as hexadecimal is, you would multiply by an increasing power of 16. Now, for this next part you might have to stretch your mind a little, unless you're like me and enjoy wierd, abstract ideas. The reason for the exact exponent of ten that you may observe, for example, in the number 567 (look up, if you've forgotten already, heh), is as follows: The number 7 is in the ones place. 10 (along with ANY other number) to the 0th power is 1. The number 60 is in the tens place. 10 to the 1st power is in the tens place. Finally, the number 500 is in the hundreds place. 10 to the 2nd power is in the hundreds place. Now you see a pattern, and now I realize that I was wrong; you didn't have to stretch your mind, heheh. Now that you hopefully understand how this system works, I'll move on to the actual use of it. This is where you have to use your new-found (or not) knowledge of hex to understand. Let us take the hex number FEDC, and convert it to dec using simple knowledge of conversions of single-digit numbers between hex and dec. Pay attention to everything here, and remember that 10 hex = 16 dec: hex- FEDC hex- (F x 10^3) + (E x 10^2) + (D x 10^1) + (C x 10^0) = dec- (15 x 16^3) + (14 x 16^2) + (13 x 16^1) + (12 x 16^0) = dec- (15 x 4096) + (14 x 256) + (13 x 16) + (12 x 1) = dec- (61440) + (3584) + (208) + (12) = dec- 65244 And if you use one of the other two methods to check this work, it is correct. The only thing limiting you from actually using this method regularly is the fact that numbers as large as these are not easily multiplied and added in your head, and I doubt you want to waste massive amounts of paper in this endeavor. This is the reason I have shown you the other methods. This method is just a way of helping you understand what exactly you're converting. Have fun, and may you find it, if not useful, at least interesting. Well, that's all that comes to mind. Hopefully it is all at least semi-clear to you now. I hope this info helps you to, at least to some extent, better understand how codes work. If you have any further questions on hexadecimal, please feel free to e-mail any one of us on the GSHI staff. This text was brought to you by GSHI.org, unless someone else gave it to you, in which case it was only written by someone at GSHI.org. Heheh.

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