Convert the decimal number 321.145 to octal and hexadecimal.



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Posted on (Answer #1)


We take integer and decimal part separately.  We devide integer part by 8 repeatedly (until we get to 0) and write the remainder:



`5=0cdot 8+5`

Reading the remainders in reverse order we get `501` which is our integer part in octal base.

Now we multiply decimal part repeatedly and write when we get integer part:












Hence when we read integer parts from top to bottom we get `1121727024ldots`

So `321.145approx501.1121727024_((8))`

To get hexadecimal number we repeat everything but with 16 instead of 8.




Hence integer part is `141`.








Hence by reading integer parts from top to bottom we get `251EB8`. Notice that numbers greater than 9 (10,11,12,13,14,15) are written as letters (A,B,C,D,E,F). Also notice that in the last line we have 8.32 and since we already had 0.32 it means that decimals `51EB8` will reapeat (this is periodic number).


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