The NOT or complement operator ( ~ ) and negative binary numbers can be confusing.
~2 = -3 because you use the formula ~x = -x - 1 The bitwise complement of a decimal number is the negation of the number minus 1.
NOTE: just using 4 bits here for the examples below but in reality PHP uses 32 bits.
Converting a negative decimal number (ie: -3) into binary takes 3 steps:
1) convert the positive version of the decimal number into binary (ie: 3 = 0011)
2) flips the bits (ie: 0011 becomes 1100)
3) add 1 (ie: 1100 + 0001 = 1101)
You might be wondering how does 1101 = -3. Well PHP uses the method "2's complement" to render negative binary numbers. If the left most bit is a 1 then the binary number is negative and you flip the bits and add 1. If it is 0 then it is positive and you don't have to do anything. So 0010 would be a positive 2. If it is 1101, it is negative and you flip the bits to get 0010. Add 1 and you get 0011 which equals -3.