NumPy Bitwise Operations

NumPy functions starting with "bitwise_" are bitwise operation functions.

NumPy bitwise operations include the following functions:

Note: You can also use operators such as "&", "~", "|", and "^" for calculations.

bitwise_and

The bitwise_and() function performs bitwise AND operation on the binary forms of integers in an array.

Example

import numpy as np

print('Binary forms of 13 and 17:')
a, b = 13, 17
print(bin(a), bin(b))
print('\n')

print('Bitwise AND of 13 and 17:')
print(np.bitwise_and(13, 17))

Output:

Binary forms of 13 and 17:
0b1101 0b10001

Bitwise AND of 13 and 17:
1

The above example can be illustrated with the following table:

The bitwise AND operation follows these rules:

bitwise_or

The bitwise_or() function performs bitwise OR operation on the binary forms of integers in an array.

Example

import numpy as np

a, b = 13, 17
print('Binary forms of 13 and 17:')
print(bin(a), bin(b))

print('Bitwise OR of 13 and 17:')
print(np.bitwise_or(13, 17))

Output:

Binary forms of 13 and 17:
0b1101 0b10001
Bitwise OR of 13 and 17:
29

The above example can be illustrated with the following table:

The bitwise OR operation follows these rules:

invert

The invert() function performs bitwise inversion on integers in an array, i.e., 0 becomes 1 and 1 becomes 0.

For signed integers, it takes the complement of the binary number and then adds 1. The highest bit of a binary number indicates its sign, with 0 being positive and 1 being negative.

Here are the steps for calculating ~1:

• Convert the original number (called the "true form") to binary.
• Bitwise inversion.
• Since the sign bit (the highest bit) is 1 (indicating a negative number), invert the other bits.
• Add 1 to get the two's complement.
• Convert back to decimal.

Example

import numpy as np

print('Bitwise inversion of 13 with dtype uint8:')
print(np.invert(np.array([13], dtype=np.uint8)))
print('\n')
# Compare the binary representations of 13 and 242 to see the inversion

print('Binary representation of 13:')
print(np.binary_repr(13, width=8))
print('\n')

print('Binary representation of 242:')
print(np.binary_repr(242, width=8))

Output:

Bitwise inversion of 13 with dtype uint8:
[242]

Binary representation of 13:
00001101

Binary representation of 242:
11110010

left_shift

The left_shift() function shifts the binary representation of array elements to the left by a specified number of positions, appending an equal number of zeros to the right.

Example

import numpy as np 

print('Shifting 10 left by two positions:')
print(np.left_shift(10, 2))
print('\n')

print('Binary representation of 10:')
print(np.binary_repr(10, width=8))
print('\n')

print('Binary representation of 40:')
print(np.binary_repr(40, width=8))
# Two bits from '00001010' are moved to the left, and two zeros are added to the right.

Output:

Shifting 10 left by two positions:
40

Binary representation of 10:
00001010

Binary representation of 40:
00101000

right_shift

The right_shift() function shifts the binary representation of array elements to the right by a specified number of positions, appending an equal number of zeros to the left.

Example

import numpy as np 

print('Shifting 40 right by two positions:')
print(np.right_shift(40, 2))
print('\n')

print('Binary representation of 40:')
print(np.binary_repr(40, width=8))
print('\n')

print('Binary representation of 10:')
print(np.binary_repr(10, width=8))
# Two bits from '00101000' are moved to the right, and two zeros are added to the left.

Output:

Shifting 40 right by two positions:
10

Binary representation of 40:
00101000

Binary representation of 10:
00001010