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poly ) input+augmentation
11100 ) letter g + 4 0s (because the poly is 5 digits, including implicit bit)
11100 ) 011001110000
^
00000
=
11001
^
11100
=
01011
^
00000
=
10111
^
11100
=
10110
^
11100
=
10100
^
11100
=
10000
^
11100
=
11000
^
11100
=
0100 <-- Remainder of 4, the checksum
Basically I take w+1 digits (which is the amount of digits in the poly, including the implicit bit) from the message. If it starts with 1, XOR the thing with the poly, otherwise, XOR it with 0. Now take the last four digits of what you have left (AKA take off the first digit because it's always 0), and bring down another digit from the original message. Now XOR again if the thing starts with 1, etc. etc., until you've brought down the last digit and XORed for the last time.
The JavaScript uses a binary push method. It checks the first bit of the remaining binary string I have, if it's 1, it XORes, if it's 0, it doesn't, etc. Then it takes off that digit. Same principle. That checks out with my manual version (which was the thing in code tags), they always return the same thing (unless I've done my math wrong in the manual version, which happens a lot. But I correct it eventually =P). Either I'm missing some mathematical steps (which is possible) or I'm not finding the right poly. I've tried all the CRC32 ones on Wikipedia, but checking my output against a CRC32 calculator didn't work. Here's my JavaScript source:
<html>
<!--------------------------------------------------------->
<head>
<title>CRC Calculator</title>
<script language="JavaScript">
// first run of the CRC function
var first_run = true;
// remove the implicit 1? (vs is it already removed)
var imp = true;
// the original divisor length.. necessary for padding 0s
var div_length = 0;
// how done is it?
var done = new Array(false,false,false);
// is the entire thing finished?
var complete = false;
// divisor/poly (without the implicit bit)
var divisor = "";
// register (CRC so far)
var register = "";
// binary code of current character
var binary = "";
// the reg text field output
var reg_output;
// the bin text field output
var bin_output;
// the table
var table;
// the input text
var file;
// pad a string to a certain length
function pad(input,length,front)
{
while(input.length < length)
{
if(front)input = "0"+input;
else input += "0";
}
return input;
}
function XOR(no1,no2)
{
var xored = "";
//convert them both to binary
no1 = no1.toString(2);
no2 = no2.toString(2);
// switch them if no1 is longer
if(no1.length < no2.length)
{
var temp = no1;
no1 = no2;
no2 = temp;
}
// go from the lowest to highest value bits until one string runs out
for(var move_up=1;move_up <= no1.length && move_up <= no2.length;++move_up)
{
// if the bits are the same, add a 0 to the beginning of xored, otherwise add a 1
if(no1.substr(no1.length-move_up,1) == no2.substr(no2.length-move_up,1)) xored = "0"+xored;
else xored = "1"+xored;
}
// once one string runs out, just tack the remaining stuff on the beginning of xored
for(var keep_going=no1.length-no2.length;keep_going>0;--keep_going)
{
xored = no1.substr(keep_going-1,1) + xored;
}
// convert to base 10 and return
return xored;
}
function crc()
{
var focus = "";
// if it is the first time, set everything up
if(first_run)
{
// set it to not the first time
first_run = !first_run;
// get the divisor
divisor = document.getElementById("poly").value;
// if it's in hex, get it in hex
if(divisor.substring(0,2) == "0x") divisor = parseInt(divisor.substring(2,divisor.length),16);
else divisor = parseInt(divisor,2);
// reset the done variables
done[0] = false;
done[1] = false;
done[2] = false;
// get the length of the divisor
div_length = divisor.toString(2).length;
}
// if the binary has been pushed to the point where we need more...
if(binary.length < div_length)
{
// if there are no chracters left, then we are done with the file
if(file.innerHTML.length == 0) done[0] = true;
// if we are not done getting characters from the input
if(!done[0])
{
// get the binary string from the next character in line...
binary += pad(file.innerHTML.charCodeAt(0).toString(2),8,true);
// ...and take that character off the assembly line
file.innerHTML = file.innerHTML.substring(1,file.innerHTML.length);
}
// if we have not already appended the extra 0s
else if(!done[1])
{
done[1] = true;
// append
for(var append=0;append<div_length-1;++append)
{
binary += "0";
}
}
// if we are completely done
else
{
done[2] = true;
binary = "DONE";
first_run = true;
}
}
// unless we are completely done
else if(!done[2])
{
// get the first bit (the highest magnitude bit)
focus = binary.substr(0,1);
var toggle = 0;
// if the focused bit is 1, XOR the binary with the divisor
if(focus == 1) toggle = pad(divisor.toString(2),binary.toString(2).length,false);
binary = XOR(binary,toggle);
// now take off the focused bit
binary = binary.substring(1,binary.length);
// set the current CRC to the binary
register = binary;
}
// output the current binary
bin_output.value = binary;
// output the current CRC
reg_output.value = "0x"+pad(parseInt(register,2).toString(16).toUpperCase(),Math.ceil((div_length-1)/4),true);
if(!done[2]) crc();
}
// initialize function for when the page loads
function init()
{
// set all the variables that point to stuff in the page
reg_output = document.getElementById("reg");
bin_output = document.getElementById("bin");
table = document.getElementById("organize");
file = document.getElementById("file");
}
</script>
</head>
<!--------------------------------------------------------->
<body onload="init()">
<table id="organize" border="0" align="center">
<tr>
<td align="left" onClick="toggle_imp()">Polynomial/Divisor (including implicit 1)</td>
<td align="center">Binary of current character</td>
<td align="right">Current CRC</td>
</tr>
<tr>
<td align="left"><input type="text" id="poly" value="11100" size="40" /></td>
<td align="center"><input type="text" id="bin" value="" /></td>
<td align="right"><input type="text" id="reg" value="" size="40" /></td>
</tr>
<tr>
<td colspan="3" align="center"><hr />Input text</td>
</tr>
<tr>
<td align="left"></td>
<td align="center"><textarea id="file" cols="75" rows="33">g</textarea></td>
<td align="right"></td>
</tr>
<tr>
<td align="left"></td>
<td align="center"><input type="button" id="button" onClick="crc()" value="Start" /></td>
<td align="right"></td>
</tr>
</table>
</body>
<!--------------------------------------------------------->
</html>
So that seems to work with my manual math. but trying all the CRC32 polys from Wikipedia and comparing my results to a CRC32 calculator got different results. Very annoying. Any help would.. help..
(hopefully) thanks
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