To convert a number from a base X, to base 10 we must first write out the number underneath its column headings in the usual “hundreds tens and units” style that you’ve come across before, let’s take for example the number 39714 which is a base 14 number:




Converting this number to base 10 is quite simple because if you look at the diagram above you can see that we have 3 “lots” of 196, 9 “lots” of 14 and 7 units:


So:



For our next example we will turn the hexadecimal number AF6E5 into base 10.  Now remember that base 16 as well as using the numbers from 0 to 9 also uses the letters A to F, so we can see that the above number is going to be quite big.  Not difficult, put the number into the 5 columns that it will take up, underneath its respective column headers and then do the basic arithmetic to arrive at the answer:



You have to remember that now that we are dealing with a base higher than 10 which is using numbers other than 0 to 9 we introduce letters to make up the difference between ‘9’ and the base itself, in which case for hexadecimal A represents 10, B represents 11, C represents 12, D represents 13, E represents 14 and finally capital F represents 15.


Bearing the above in mind:



So even converting large numbers like hexadecimal isn’t that difficult, provided you keep your wits about you and make sure that you do the multiplications and the final adding up correctly.