How do you convert numbers to any base

Are the rules for converting different bases the same or different?

I'm having a hard time figuring these out...

Change 101110 Base 2 to Base 8

Change 6210 Base 7 to base 9

Add 36 base 8 to 11011 base 2

Can you explain to me step by step? Help would be much appreciated!!! Thanks in advance!

Base 2 and base 8 is a special case because
8 is 2^3 ... each 3 digits in binary (base 2)
represents one digit in octal (base 8)

binary .... 101 110
octal . .. . . 5 ... 6
since 5 = 1x2^2 + 0x2^1 + 1x2^0 = 4+1
and similarly for 6
Answer: 56
(the decimal equivalent is 46, since 5*8 + 6 = 40+6 = 46,
which in base 2 = 1011110 = 32 + 8 + 4 + 2)

For the last one:
Octal .. . . 3 . . . 6
Binary ..011 ...110
(Decimal value 30, since 3*8 + 6 = 24 + 6 = 30)

Base 7 to base 9 is not so easy.

One way is to go through base 10.

6210 base 7 =
6 x 7^3 +
2 x 7^2 +
1 x 7^1 +
0 =
6 * 343 = 2058
2 * 49 = 98
1 * 7 = 7
and sum = 2163 base 10

To convert to base 9, you can use the "backwards remainders" method:

2163 / 9 = 240 remainder 3
240 / 9 = 26 remainder 6
26 / 9 = 2 remainder 8
2 / 9 = 0 remainder 2

So the answer in base 9 is those remainders, backwards: 2863

2 * 9^3 + 8 * 9^2 + 6 * 9^1 + 3 * 9^0 =
2 * 729 + 8 * 81 + 6 * 9 + 3 * 1 =
1458 + 648 + 54 + 3 = 2163

You could use this method to convert directly from base 7 to base 9,
but then you would have to do the divisions in base 7.