For example, in PHP, how would I reverse the bits of the byte 11011111 to 11111011?
Check the section on reversing bit sequences in Bit Twiddling Hacks. Should be easy to adapt one of the techniques into PHP.
While probably not practical for PHP, there's a particularly fascinating one using 3 64bit operations:
unsigned char b; // reverse this (8-bit) byte
b = (b * 0x0202020202ULL & 0x010884422010ULL) % 1023;