Convert 0.4304 fraction to base 3

[Nipuna]

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.

[SemiconductorCat]

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.

[Nipuna]

Thank you very much

But I prefer multiplication method it's easier than this to me

[SemiconductorCat]

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-

[Nipuna]

Really good advice, thank you very much.

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

Thansk

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