Break up numbers in any system into a polynomial-like expression to see what it really means. When we see a number such as 333, all the 3's are really different. The different positions make the symbols mean 3, 30 and 300. The number 333 is really 3 + 3 X 10 + 3 X 10^2. The system is even clearer when 333 is written as 3 X 10^0 + 3 X 10^1 + 3 X 10^2. Ten is the standard base, but other bases are sometimes appropriate. Computers prefer the base 2, so 1101 means 1 X 2^0 + 0 X 2^1 + 1 X 2^2 + 1 X 2^3 = 1 + 0 + 4 + 8 = 13. There are standard algorithms for translating into and out of base 10.
Translate a number written in another base into base 10 by multiplying each digit by the appropriate power of the base. For example, translate the base 8 number 243 by multiplying each digit by the power of 8 that corresponds to its position: 3 X 8^0 + 4 X 8^1 + 2 X 8^2 = 3 X 1 + 4 X 8 + 2 X 64 = 3 + 32 + 128 = 163 base 10.
Change base 10 numbers into another base by a series of divisions. Divide the base into the number, and keep both the quotient and the remainder. The remainder will be the rightmost digit of the number in the new base. Divide the base into the quotient, and keep the quotient and remainder. Repeat the previous step until the quotient is zero. The translation will be -- from right to left -- the saved remainders in the order they appeared. Translating 123 into base 5 looks like this: 123/5 = 24 with remainder 3. 24/5 = 4 with remainder 4. 4/5 = 0 with remainder 4. So 123 base 10 is 443 base 5.