Convert 0.4304 fraction to base 3

Mathematics for Computing
Post Reply
User avatar
Nipuna
Moderator
Moderator
Posts: 2729
Joined: Mon Jan 04, 2010 8:02 pm
Location: Deraniyagala,SRI LANKA

Convert 0.4304 fraction to base 3

Post by Nipuna » Fri Jan 06, 2012 11:31 am

I've finished my 1st subject of BIT which is Information System

Now I am studying Computer Systems 1, Here is the subject that I get questions. ;)

So here goes my first question. I tried to figure this out also tried searching in the internet but couldn't find the way of solving this, There is an example in the book but I can't figure it out. :?

Convert 0.430410 to base 3 by subtracting.

Please Help me to solve this.



Thanks

Edit:-- It's OK I was able to solve this by using multiplication method. But I like if you can show me the other way of solving too.
User avatar
SemiconductorCat
Major
Major
Posts: 455
Joined: Mon Aug 22, 2011 8:42 pm
Location: currently in hyperspace

Re: Convert 0.4304 fraction to base 3

Post by SemiconductorCat » Fri Jan 06, 2012 10:18 pm

you may asking about repeated subtraction method right?

well ,
1/3 = 0.333333...
2/3 = 0.666666.....
1/9 = 0.111111...
2/0 = 0.2222222....
1/27=0.03703703703703703703703703703704...
2/27 = 0.01575.....

...

1/3^n = -------
2/3^n = ---------

like that .



what you have to write.

==> 0.4304(base10) = 0 + (a1) 3^-1 + (a2) 3^-2 + (a3) 3^-3 + .... + (an) 3^-n

and a1,a2,a3 .... an can be 0,1 or 2 in value.

so simply , we can easily see that 0.4304 is greater than 0.33333... and less than 0.6666... so
a1 = 1 and subtract 0.3333.. from it.

likewise you can continue it up to n.


PS: note that if you are going to implement this in a computer/micro-controller or a microprocessor please
don't use this method. This method is rely on heavy use of the floating point operations.
User avatar
Nipuna
Moderator
Moderator
Posts: 2729
Joined: Mon Jan 04, 2010 8:02 pm
Location: Deraniyagala,SRI LANKA

Re: Convert 0.4304 fraction to base 3

Post by Nipuna » Sat Jan 07, 2012 7:47 am

Thank you very much

But I prefer multiplication method it's easier than this to me ;)
User avatar
SemiconductorCat
Major
Major
Posts: 455
Joined: Mon Aug 22, 2011 8:42 pm
Location: currently in hyperspace

Re: Convert 0.4304 fraction to base 3

Post by SemiconductorCat » Sat Jan 07, 2012 4:13 pm

use any method that you wish. :)


But understand the basic fundamental.

if you know why we divide when finding decimals and we multiply when we want to find fractions, then
you don't need to memorize any method either.

Reading a book like http://www.amazon.com/Hackers-Delight-H ... 0201914654 is recommended
too to know about more numerical methods in computing. Studying more depth those are more wise, because
every engineering student is taking a course called real analysis and numerical methods. Not only in CS but
everywhere in engineering.

Dig on how the logarithms are found on base ten , a similar method is used in calculation. The same principle.
Take you time and think. More concentrate you can do it.It's worth time you spending on it.


It's worth to dig it.

-sandun-
User avatar
Nipuna
Moderator
Moderator
Posts: 2729
Joined: Mon Jan 04, 2010 8:02 pm
Location: Deraniyagala,SRI LANKA

Re: Convert 0.4304 fraction to base 3

Post by Nipuna » Sat Jan 07, 2012 7:17 pm

Really good advice, thank you very much.

And by the way I know all number systems work exactly same as Decimal numbers.

Thansk

[ Post made via Mobile Device ] Image
Post Reply

Return to “Mathematics”