Bit Manipulation

Two's Complement binary for Positive Integers:

• 0 is written as "0"

• 1 is written as "1"

• 2 is written as "10"

• 3 is "11"

• 4 is "100"

• 5 is "101"

• .

• .

• 1029 is "10000000101" == 2**10 + 2**2 + 2**0 == 1024 + 4 + 1

The Operators:

x << y Returns x with the bits shifted to the left by y places (and new bits on the right-hand-side are zeros). This is the same as multiplying x by 2**y.

x >> y Returns x with the bits shifted to the right by y places. This is the same as //'ing x by 2**y.

x & y Does a "bitwise and". Each bit of the output is 1 if the corresponding bit of x AND of y is 1, otherwise it's 0.

x | y Does a "bitwise or". Each bit of the output is 0 if the corresponding bit of x AND of y is 0, otherwise it's 1.

~x Returns the complement of x - the number you get by switching each 1 for a 0 and each 0 for a 1. This is the same as -x - 1.

x ^ y Does a "bitwise exclusive or". Each bit of the output is the same as the corresponding bit in x if that bit in y is 0, and it's the complement of the bit in x if that bit in y is 1.