Hexidecimal to base 10
The hexadecimal numeric system works the same way that base 10 does. the only thing that makes it more confusing is the fact that most people are not used to counting in a different.
All that you have to rememberis that all number system work in the same way. you just have to find place values. this may sound like something that your grade 3 teacher told you and this is because it is. this is the same tedious process that you used all those years ago and probably forgot. if this is the case then I am here to help you remember.
all you have to do is look at a number such as 243 and see that it is just made up of 3 separate components or pieces. It can also be written as 200+43+3 so as you can see there is a 2 in the 3rd column. This value is 100 x 2. There is a 4 in the 2nd collum which in turn stands for 10 x 3. Finally the 1st collum stands for 1 x 3.
So if you were to apply this to the hexadecimal system you just have to remember that it works on a differnet value system. The valuses go like this
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
This could be continues to show that 10 = 16 and 11 = 17 . . . .ect. But that is unneccisary. This also means that each collum is equal to a different power of 16. the powers progress in normal base 10 fasion 1,2,3,4,5. . . .
But what does any of this have to do with the place values. Well if i take the hexadecimal number AF1 andbreak it down so that i can findthe base 10 value of it i would first have to find the individual values of each of the digits. I would take the 1st column and multiply it by 1 like i did be for and i will get 1 x 1. This means that the first digit is equal to a base 1o value of 1. the next column is again the same. It is the next columnthat is a little bit harder. The second column is equal to 16 to the power of 1. So this means that you take the base 10 value of F and times it by 16 . This translate into 16 x 15 giving you a base 10 value of 240. The last column is equal to a value of 16 squared. This becomes a base 10 value of 256. This becomes 256 x A or 256 x 10. This equals 2560. so now that we have all the separate values that are needed to find the total base 10 value of AF1 all you have to do is add them together and the end result is 2801.
