The Modern C++ Challenge

10. Gray code

Gray code, also known as reflected binary code or simply reflected binary, is a form of binary encoding where two consecutive numbers differ by only one bit. To perform a binary reflected Gray code encoding, we need to use the following formula:

if b[i-1] = 1 then g[i] = not b[i]else g[i] = b[i]

This is equivalent to the following:

g = b xor (b logically right shifted 1 time)

For decoding a binary reflected Gray code, the following formula should be used:

b[0] = g[0]b[i] = g[i] xor b[i-1]

These can be written in C++ as follows, for 32-bit unsigned integers:

unsigned int gray_encode(unsigned int const num){   return num ^ (num >> 1);}unsigned int gray_decode(unsigned int gray){ for (unsigned int bit = 1U << 31; bit > 1; bit >>= ...