I would like a working implmentation of JavaScript code to convert
arbitarily large decimal integers to hex and to convert the hex back
to decimal.
For example: a HTML form with an input field, a user could type in a
large number: "1234567890123456789012345678901234567890" and press a
button and another field will display the Hexidecimal equivalnt and
another field will use that hex to convert back to decimal in another
field

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Clarification of Question by ricjohnsoniii-ga on 10 May 2005 17:23 PDT

Note:  Simply re-creating long division by hand in NOT acceptable.  I
am looking for the MAGIC number (sort of like how square roots are
implmented in binary with the magic number of 20).
I have found a working code up to 10 digits with the magic number of
5, but when I multiply 5 by the remainder, I get an overflow, so I
need a way to re-implment the magic number on Large numbers again.

I am not sure what you mean by "magic number".  It looks like you
might be referring to the following algorithm for square root:
http://www.dattalo.com/technical/theory/sqrt.html
As the author notes, the algorithm is similar to long division, so I
can't see why you object to using long division.

might this help you?

http://www.permadi.com/tutorial/numConvJs/

It's a nice number converter from / to - Dec/Bin/Hex that converts
your number as you type it. I tried it with some numbers I have and it
worked fine.

I.

Regarding http://www.permadi.com/tutorial/numConvJs/

This number converted is limited to 15 digits.  It uses the internal
MATH methods and native data types to convert to HEX.  I am looking
for something that can convert a LARGE number - assume at least 30
digits.

Here's some code I just cooked up.  Should do the trick.  No magic numbers though.


/************************************************
 * This function decodes a decimal string and
 * returns a hexadecimal string.  There is no
 * size limit on the decimal input.
 ************************************************/
function dec2hex(dec)
{
	//Create a buffer for the hexadecimal
	var hex = new Array(
	Math.ceil(
		dec.length * 0.83048202372184058696757985737235
	));
	
	//Initialize as 0
	for(var i=0; i<hex.length; i++)
		hex[i] = 0;
	
	//Create raw binary number in hex
	for(var i=0; i<dec.length; i++)
	{
		//Multiply by 10
		for(var j=0; j<hex.length; j++)
			hex[j] *= 10;
		
		//Add character
		hex[0] += parseInt(dec.charAt(i));
		
		//Carry
		for(var j=0; j < hex.length; j++)
			if(hex[j] > 16)
			{
				hex[j + 1] += Math.floor(hex[j] / 16);
				hex[j] = hex[j] % 16;
			}
	}
	
	//Convert raw binary to hex
	var hex_chars = "0123456789abcdef";
	
	//Strip leading zeros
	var index = hex.length - 1;
	while(hex[index] == 0 && index > 0)
		--index;
	
	//Append the hexadecimal digits
	var result = hex_chars.charAt(hex[0]);
	for(var i=1; i <= index; i++)
		result = hex_chars.charAt(hex[i]) + result;
		
	//Done
	return result;
}

I am sorry, I tried to code this, but it did not work for LARGE
numbers (50+ digits). Can you clarify the code with comments for each
step (I may have coded it wrong).
1) Does the step "//Multiply by 10" encounter an overflow?
2) Why do you work from the lwft (signigicant digits)?
3) This seems the same as long division - can you explain?