Time for action – twiddling bits

We will now cover three tricks—checking whether the signs of integers are different, checking whether a number is a power of 2, and calculating the modulus of a number that is a power of 2. We will show an operators-only notation and one using the corresponding NumPy functions:

1. The first trick depends on the XOR or ^ operator. The XOR operator is also called the inequality operator; so, if the sign bit of the two operands is different, the XOR operation will lead to a negative number (see https://www.khanacademy.org/computing/computer-science/cryptography/ciphers/a/xor-bitwise-operation).

   The following truth table illustrates the XOR operator:

   Input 1	Input 2	XOR
   True	True	False
   False	True	True
   True	False	True
   False	False	False

   The ^ operator corresponds to the bitwise_xor() function, and the < operator corresponds to the less() function:

   x = np.arange(-9, 9)
   y = -x
   print("Sign different?", (x ^ y) < 0)
   print(&quot...