calculating between numeral systems

[Justa Lol]

calculating from decimal to octal, hexadecimal or binary is easy... but the opposit way is harder, could someone tell me a way to calculate from octal to decimal?

like from decimal to octal:

lets say 11 decimal to octal

11/8 = 1 rest 0.375
1/8 = 0 rest 0.125

0.375 * 8 = 3
0.125 * 8 = 1

so result: 11 decimal is 13 in octal...

[jemidiah]

The other way is actually the easy way.

Take a base 10 number. Index the digits by writing the number as a_n a_n-1 ... a₀. This number is equal to a_n*10ⁿ+a_n-1*10^n-1+...+a₀*10⁰. As an example, 457 gives us a_2 = 4, a_1 = 5, a_0 = 7, and the expression above gives 4*10^2 + 5*10 + 7 = 457.

Doing the same thing in other bases turns out to be easy. If we have the base 8 digits of a number, index them as above, and then we have

a_n a_n-1 ... a₀ = a_n*8ⁿ+a_n-1*8^n-1+...+a₀*8⁰

Using your example of 11 in decimal being 13 in octal, take a_1 = 1, a_0 = 3, and simply do 1*8^1 + 3*8^0 = 13. Since we're doing arithmetic in base 10, our final answer comes out as a base 10 number. If you're familiar with converting from binary to decimal, you do the same thing. In octal, the rightmost place is the "1's" digit, the next place is the "8's" digit, the next is the "64's" digit, etc. In base 10, we analogously have the "1's", "10's", and "100's" digits.