float conversion logic
Author 
Message 
Insectoid

Posted: Fri Dec 19, 2008 12:04 pm Post subject: float conversion logic 


So, I just want some confirmation on my float conversion logic.
I am writing a program to convert a float to another number system. I have managed to separate the float into 2 parts (5.9 => 5, 9). My method for converting the decimal is to flip it over (053 => 350), then convert it in the same manner as an integer, using div and mod, but attach the result backwards again. Is this logic correct? so 50.05 converted to hex would be 32.23?
code, with comments at key points:
Ruby: 
require 'jcode'
class NumberConverter
attr_reader :decimal
def initialize (number, base)
@number = number
@base = base
@integer = @number.to_i #the integer portion of the float
@decimal = (@number.to_s.split(".")[1]).reverse.to_i #the decimal portion of the float, flipped
end
def to_base(base)
chars =("0".."9").to_a+("A".."Z").to_a
answer = ""
temp = @integer
until (temp == 0) do
answer = chars[(temp %base)] + answer #adds to front of answer
temp /= base
end
temp = @decimal
answer += "."
until (temp == 0) do
answer += chars[(temp %base)] #adds to back of answer
temp /= base
end
answer.empty? ? "0" : answer
end
end
puts (NumberConverter.new(50.05 s, 10).to_base(16))

Now, either my logic is wrong or I have executed it wrong, or it is correct and I just don't know it. The difficulty is, I don't know what the correct answer is, and it's hard to check, because there aren't too many float converters out there (lots of integer ones though). 





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OneOffDriveByPoster

Posted: Fri Dec 19, 2008 12:46 pm Post subject: Re: float conversion logic 


50.05 in hex = ?
50 in hex: 32
.05 in hex = ?
5 / 100
5h / 64h
Long division
code:  0.0CCC...
64 5 00
500 
You are looking for 32.0CCC... 





Tyr_God_Of_War

Posted: Fri Dec 19, 2008 9:03 pm Post subject: RE:float conversion logic 


You know, the calculator that comes with windows can't do that. It just rounds. That ruins my cunning plan of using it to check your work. Maybe another, better calculator can... 





Insectoid

Posted: Sun Dec 21, 2008 2:31 pm Post subject: RE:float conversion logic 


Well, I'm not on windows, and so don't have access the that calculator, even if it did work. The calculator that comes with mac is worse than the windows one. 





OneOffDriveByPoster

Posted: Sun Dec 21, 2008 2:55 pm Post subject: Re: RE:float conversion logic 


Tyr_God_Of_War @ Fri Dec 19, 2008 9:03 pm wrote: You know, the calculator that comes with windows can't do that. It just rounds. That ruins my cunning plan of using it to check your work. Maybe another, better calculator can... Try
320CCCCCCCCCCCCC
/100000000000000
in decimal:
3606482581598293196 / 72057594037927936
= 50.049999999999999988897769753748 approx.
(This was done with the Windows calculator.) 





Insectoid

Posted: Wed Dec 24, 2008 11:21 am Post subject: RE:float conversion logic 


So, I would have to divide the number by the base equivalent of 100? so to octal would be 5/144, and to binary would be 101/1100100. Right? 





OneOffDriveByPoster

Posted: Wed Dec 24, 2008 12:03 pm Post subject: Re: float conversion logic 


Well 0.05 = 5/100.
You could do 1/20...
Converting from hex or oct to binary and vice versa is much simpler of course.
8 = 2^3 so an oct digit is 3 bits
16 = 2^4 so a hex digit is 4 bits
Here is the binary case.
code:  v v
0.000011001
1100100 101 00000 <==
11 00100
1 111000
1 100100
10100000 <==
1100100 






Insectoid

Posted: Wed Dec 24, 2008 12:08 pm Post subject: RE:float conversion logic 


I just though of something...
In base 10, you can multiply a decimal by 10 multiple times to make it >1. So, for hex, could I multiply by 16^length to make it >0, convert, then divide by 16^length again? Just a thought... 





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OneOffDriveByPoster

Posted: Wed Dec 24, 2008 12:23 pm Post subject: Re: RE:float conversion logic 


Exactly:
If you consider using multiplication, which the division process
implies when you "add zeros".
For each digit after the ones digit, you can multiply by the base to see
what the value of the digit is by taking the nonfractional part.
This is obvious using base10.
code:  0
.
0 0.05 * 10 = 0.5
5 0.5 * 10 = 5  0.05 = 0.05 (as expected)
code:  0
.
0 0.05 * 2 = 0.1
0 0.1 * 2 = 0.2
0 0.2 * 2 = 0.4 <==
0 0.4 * 2 = 0.8
1 0.8 * 2 = 1.6
1 0.6 * 2 = 1.2
0 0.2 * 2 = 0.4 <==  0.05 = 0.0000110011001100...
(This is what we got from long division too.)
code:  0
.
0 0.05 * 16 = 0.8
C 0.8 * 16 = 12.8 <==
C 0.8 * 16 = 12.8 <==  0.05 = 0.0CCC...
(This is what we got from long division too.) 





OneOffDriveByPoster

Posted: Wed Dec 24, 2008 12:28 pm Post subject: Re: RE:float conversion logic 


insectoid @ Wed Dec 24, 2008 12:08 pm wrote: I just though of something...
In base 10, you can multiply a decimal by 10 multiple times to make it >1. So, for hex, could I multiply by 16^length to make it >0, convert, then divide by 16^length again? Just a thought... You need to keep the remainder and deal with it. The multiplying process above is basically this. 





Insectoid

Posted: Wed Dec 24, 2008 8:34 pm Post subject: RE:float conversion logic 


I got it! Multiply the number by target base^number of decimal places, divide by target base equivalent of 100 (64, 144, etc.), and then divide by base^number of decimal places. I think there's something missing, but I'm not sure... 






