Gray code to binary conversion

Question

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.

@sunmoon: If your answer gives the algorithm, what do you need help with? — Jeremiah Willcock, Feb 27 '11 at 04:41
@sunmoon, if the input strings are short enough, there's always lookup tables. :) — sarnold, Feb 27 '11 at 05:00
@sarnold: If the input string is large, generating the lookup table is time consuming operation right? — sunmoon, Feb 27 '11 at 05:09
@sunmoon: long input strings are probably very expensive to precompute and store tables compared to your algorithm below. — sarnold, Feb 27 '11 at 06:17

score 2 · Accepted Answer · answered Feb 27 '11 at 04:36

2

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

answered Feb 27 '11 at 04:36

sunmoon

1,448
1
15
27

if this is the answer to your own question then mark it as answer :) – JohnIdol Mar 01 '11 at 13:20
Warning - this answer is slightly incorrect. The correct formula for Bn-1 is `Bn-1 = Bn XOR Gn-1`. See [here](http://books.google.ca/books?id=MfapI7UIr9YC&lpg=PA51&ots=IKd__7XXio&dq=bn-1%20%22gray%20code%22%20gn&pg=PA50#v=onepage&q=bn-1%20%22gray%20code%22%20gn&f=false) for more info. – Scott Whitlock Jun 16 '11 at 17:26

score 0 · Answer 2 · answered Nov 15 '16 at 10:03

0

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/

answered Nov 15 '16 at 10:03

Chad Davis

27
7

score 0 · Answer 3 · answered Nov 25 '17 at 06:21

<?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));

?>

Gray code to binary conversion

3 Answers3