Shift operation

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.

# 1 & odd/even
In[1]:  1 & 1
Out[1]: 1
In[2]:  1 & 2
Out[2]: 0
In[3]:  1 & 3
Out[3]: 1
In[4]:  1 & 4
Out[4]: 0
In[5]:  1 & 5
Out[5]: 1
In[6]:  1 & 6
Out[6]: 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.