<ahref="https://en.wikipedia.org/wiki/Gray code"target="_blank">Gray code</a> is a form of binary encoding where transitions between consecutive numbers differ by only one bit.
It is also useful for generating inputs for <ahref="https://en.wikipedia.org/wiki/Karnaugh map"target="_blank">Karnaugh maps</a> in order from left to right or top to bottom.
Create a function to encode a number to and decode a number from Gray code. The function should will have 2 parameters.
The first would be a boolean. The function should encode for true and decode for false. The second parameter would be the number to be encoded/decoded.
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):
<pre>
if b[i-1] = 1
g[i] = not b[i]
else
g[i] = b[i]
</pre>
Or:
<pre>
g = b xor (b logically right shifted 1 time)
</pre>
Decoding (MSB is bit 0, b is binary, g is Gray code):