21-Feb-2012, 8:09 PM
Quote:I have no idea what the heck base systems are
It's not hard. We use the decimal or base 10 system. In this system there are 10 digits, 0 through 9, representing each number less than 10. Each number N is represented by a list of digits, which are determined by finding d_1, d_2 etc. such that N = d_1 + 10*d_2 + 100*d_3 + 1000*d_4 + ... and so on until we reach a power of 10 larger than N. We write numbers using this series of digits in opposite order from how I wrote them there.
Ex: 1028 is 1*1000 + 0*100 + 2*10 + 8
In an alternative base system it's the same thing, only 10 is replaced by some other number, and there are a different number of digits, which may be represented by some smaller set of numbers or it might have 0-9 plus extra symbols if the base is larger than 10.
Ex: In base 2, one has the digits 0 and 1 representing the numbers less than 2. A number can be represented in binary with digits d_1, d_2 etc. such that N = d_1 + 2*d_2 + 4*d_3 + 8*d_4 + ... and so on until we reach a power of 2 greater than N. Remember that these d's are required to be 0 or 1, they are not allowed to be anything else.
234 in binary, for example, would be 1*128 + 1*64 + 1*32 + 0*16 + 1*8 + 0*4 + 1*2 + 0*1, so we would write it as 11101010.
The base 2 system is very popular because it is used by computers to represent numbers, because computers store and operate on data as a series of on/off states, which are made to represent numbers in binary.