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.
 
GrayEncode <- function(binary) {
	gray <- substr(binary,1,1)
	repeat {
	if  (substr(binary,1,1) != substr(binary,2,2)) gray <- paste(gray,"1",sep="")
	else gray <- paste(gray,"0",sep="")
	binary <- substr(binary,2,nchar(binary))
	if (nchar(binary) <=1) {
		break
		}
	}
return (gray)
}
GrayDecode <- function(gray) {
	binary <- substr(gray,1,1)
	repeat {
	if  (substr(binary,nchar(binary),nchar(binary)) != substr(gray,2,2)) binary <- paste(binary ,"1",sep="")
	else binary <- paste(binary ,"0",sep="")
	gray <- substr(gray,2,nchar(gray))
 
	if (nchar(gray) <=1) {
		break
		}
	}
return (binary)
}
 