How do you convert Hexadecimal to octal?

Formally, to convert from any base to any other base, you repeatedly divide by the second base, truncating down to the nearest integer, and recording the remainders in each step, until the result is zero. Then you write the remainders in reverse order. It is important to realize that the divisions must be done using the rules of arithmetic in the first base As an example, converting 12A 16 to 452 8 follow the steps (everything not suffixed is base 16) 12A / 8 is 37 remainder 2 37 / 8 is 4 remainder 5 4 / 8 is 0 remainder 4 - the answer is 452 8 Alternatively, since hexadecimal and octal are even multiples of base 2 or binary, you can convert by writing down the base 16 in binary, which you can do by inspection, regrouping in groups of 3, and then converting to base 8 12A = 0001 0010 1010 000 100 101 010 = 452 A larger example, showing all possible digits 0123456789ABCDEF = 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 0 000 000 100 100 011 010 001 010 110 011 110 001 001 101 010 111 100 110 111 101 111 = 0004432126361152746757.

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