Given a gray code for a number, find the binary code for the number.
Gray code is a binary numeral system where two successive values differ in only one bit.
For Example two bit gray code is: 0 - 00 1 - 01 2 - 11 3 - 10
Binary is:
0 - 00 1 - 01 2 - 10 3 - 11
Provide an algorithm to convert the gray code of the number to binary code.
For example, input is 11. Expected output is 10.
Converting the Gray code to binary is:
Retain the Most significant bit as it is and for the rest of the bits keep xoring the successive bits.
ie Gn Gn-1 Gn-2 ........ G1 is the gray code and Bn Bn-1 .......B1 is the binary code.
Bn= Gn and for all the other bits Bn-1 = Gn-1 XOR Gn
Bn-1 = Bn XOR Gn-1. See here for more info.If you want an easy way there is a good online gray code converter that you can use: http://www.convertforfree.com/gray-code-converter/
<?php
function gry_code($n) {
if($n == 0 || $n > 65 ) {
return "Invalid input please input between 1 to 65";
exit;
}
$arr = array();
array_push($arr,"0","1");
$i = 0;
$j = 0;
for ($i = 2; $i < (1<<$n); $i = $i<<1)
{
//duplicate the arr contents in reverse order
for ($j = $i-1 ; $j >= 0 ; $j--)
array_push($arr,$arr[$j]);
// append 0 to the first half
for ($j = 0 ; $j < $i ; $j++)
$arr[$j] = "0".$arr[$j];
// append 1 to the second half
for ($j = $i ; $j < 2*$i ; $j++)
$arr[$j] = "1".$arr[$j];
}
//return $arr;
$arr = array_slice($arr, -$n);
foreach($arr as $key => $arrx) {
echo $arrx."\n";
}
//return $arr;
}
print_r(gry_code(5));
?>
