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Convert the decimal number 321.145 to octal and hexadecimal.
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High School Teacher
We take integer and decimal part separately. We devide integer part by 8 repeatedly (until we get to 0) and write the remainder:
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`
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).
Posted by tiburtius on January 22, 2013 at 5:39 PM (Answer #1)
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