a) What is 01010101010101010101010? You say "number" but that is fast and loose.
$a = 010101010101010101010101010 gets treated as an octal representation of a number (leading zero). If it is bigger than the max integer value, you get a float back, not an integer.
$b = 1010101010101010101010101010 gets treated as a decimal representation of a number (no leading zero). If it is bigger than the max integer value, you get a float back, not an integer.
$c = "010101010101010101010101010" gets treated as a string, and each character takes 8 bits... so you are not doing bit manipulation at all, you are manipulating substrings within a string.
b) Be careful of bit manipulation in php, particularly shifts. There is no unsigned integer in php, thus the results in php don't generally match the results in a compiled program language.
c) MySql permits the storage of unsigned integers but that really doesn't do you any good because you can't have an unsigned integer in php.
So, if you are talking true bit manipulation, you are talking 4 bytes of data for 32 bits, which is of type integer in both php and mysql.