How you convert binery to octal?

Answer 1

To convert any number from any base to any other base, simply iteratively divide the number by the target base using the rules of arithmetic for the first base, recording the remainders in reverse order, until the result is zero.

For example, converting 0111011011102 to 35568 is as follows...

Note: Everything is expressed in binary, so I will omit the base 2 symbol

011101101110 / 1000 is 011101101 remainder 110

011101101 / 1000 is 011101 remainder 101

011101 / 1000 is 011 remainder 101

011 / 1000 is 0 remainder 011

So the answer is (011)(101)(101)(110) or 3556

Special Case:

Since we are converting from binary to a base that is a power of 2, we can also use the grouping trick, because dividing by 1000 is simply right shifting by 3.

011101101110 grouped by 3 is 011 101 101 110 or 3556.

This works for hexadecimal as well.

011101101110 grouped by 4 is 0111 0110 1110 or 76E.