123 in base 4 and 123 in base 10 are most certainly different. In base 4 from right to left, each place is worth 1, then 4, then 16, then 64, etc. In base 10 from right to left, each place is worth 1, then 10, then 100, then 1000, etc. In each base, each placeholder (excluding the very right one) is worth the previous placeholder multiplied by the base. The very right placeholder is always worth 1. So to use your example of 123 in base 4, you would add 3 (3 x 1) plus 8 (2 x 4) plus 4 (1 x 4) and the result is 15 decimal. I'm not always the best at explaining things so I'm sorry if this confuses you. If so, keep the questions coming, we'll get you straightened out. The only coversions I usually do are between hex, binary and decimal. Converting between binary and hex is a snap and my method shown above will get you to and from decimal easily. In school we were told the most fool-proof way is to take everything through binary, I can't say I agree though.