Gray code
Karnaugh maps
Create functions to encode a number to and decode a number from Gray code.

Display the normal binary representations, Gray code representations, and decoded Gray code values for all 5-bit binary numbers (0-31 inclusive, leading 0's not necessary).

There are many possible Gray codes. The following encodes what is called "binary reflected Gray code."

Encoding (MSB is bit 0, b is binary, g is Gray code):

if b[i-1] = 1
   g[i] = not b[i]
else
   g[i] = b[i]
Or:

g = b xor (b logically right shifted 1 time)
Decoding (MSB is bit 0, b is binary, g is Gray code):

b[0] = g[0]

for other bits:
b[i] = g[i] xor b[i-1]
Reference
 Converting Between Gray and Binary Codes. It includes step-by-step animations.
 
<?php
 
/**
 * @author Elad Yosifon
 */
 
/**
 * @param int $binary
 * @return int
 */
function gray_encode($binary){
	return $binary ^ ($binary >> 1);
}
 
/**
 * @param int $gray
 * @return int
 */
function gray_decode($gray){
	$binary = $gray;
	while($gray >>= 1) $binary ^= $gray;
	return $binary;
}
 
for($i=0;$i<32;$i++){
	$gray_encoded = gray_encode($i);
	printf("%2d : %05b => %05b => %05b : %2d \n",$i, $i, $gray_encoded, $gray_encoded, gray_decode($gray_encoded));
}
 