Can binary numbers be converted to octal?

Answer 1

Yes. There are two methods.

Formally, to convert any number from any base to any other base, simply iteratively divide by that other base, using the rules of arithmetic of the first base, recording remainders in reverse order, until the quotient is zero. For instance, to convert 10111112 to 1378 start by dividing by 10002 and repeating...

10111112 divided by 10002 = 101112 remainder 1112

10112 divided by 10002 = 12 remainder 112

12 divided by 10002 = 02 remainder 12

The answer is 1 (12) 3 (112) 7 (1112)

The second method depends on the fact that 2 and 8 are relative powers of each other, specifically that 8 is 2 to the third power. As a result, you can take the binary bits and group them into groups of three bits and convert them on sight. 10111112 can be rewritten as 12 0112 1112. This, however, is only a trick for a human being; a computer still needs to do the division, but you could use the trick for a computer with a look up table. We also use the trick when converting for hexadecimal, but we cannot use the trick for decimal, because the divisor is 10102, and not just one 1 followed by some number of zeros.