NumPy: Convert a given vector of integers to a matrix of binary representation

Last update on August 29 2025 12:45:18 (UTC/GMT +8 hours)

Convert integer vector to binary matrix.

Write a NumPy program to convert a given vector of integers to a matrix of binary representation.

Pictorial Presentation:

Python NumPy: Convert a given vector of integers to a matrix of binary representation

Sample Solution:

Python Code:

# Importing the NumPy library
import numpy as np

# Creating a NumPy array 'nums' containing a set of integers
nums = np.array([0, 1, 3, 5, 7, 9, 11, 13, 15])

# Displaying the original vector 'nums'
print("Original vector:")
print(nums)

# Creating a binary representation of 'nums' using bitwise operations and reshaping
# The resultant array represents the binary representation of each element in 'nums'
bin_nums = ((nums.reshape(-1, 1) & (2 ** np.arange(8))) != 0).astype(int)

# Displaying the binary representation of the vector 'nums'
print("\nBinary representation of the said vector:")
print(bin_nums[:, ::-1])  # Reversing the columns to display binary digits in the correct order

Sample Output:

Original vector:
[ 0  1  3  5  7  9 11 13 15]

Binary representation of the said vector:
[[0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 1]
 [0 0 0 0 0 0 1 1]
 [0 0 0 0 0 1 0 1]
 [0 0 0 0 0 1 1 1]
 [0 0 0 0 1 0 0 1]
 [0 0 0 0 1 0 1 1]
 [0 0 0 0 1 1 0 1]
 [0 0 0 0 1 1 1 1]]

Explanation:

In the above exercise -

nums = np.array([0, 1, 3, 5, 7, 9, 11, 13, 15]): Creates a Numpy array with specified values.

bin_nums = ((nums.reshape(-1,1) & (2**np.arange(8))) != 0).astype(int)

In the above code -

nums.reshape(-1,1): Reshapes nums into a 2D column array of shape (9, 1).
2**np.arange(8): Creates an array of powers of 2 from 2^0 to 2^7.
nums.reshape(-1,1) & (2**np.arange(8)): Applies the bitwise AND operation between the reshaped nums array and the powers of 2 array using broadcasting. This operation is a way to extract the binary digits for each number in nums.
((nums.reshape(-1,1) & (2**np.arange(8))) != 0): Compares the result of the bitwise AND operation with 0. If the result is not equal to 0, it returns True; otherwise, it returns False.
((nums.reshape(-1,1) & (2**np.arange(8))) != 0).astype(int): Converts the boolean array obtained in the previous step into an integer array, where True becomes 1 and False becomes 0. This array represents the binary representation of the numbers in nums, but the order of the bits is reversed.

bin_nums[:,::-1]: Reverses the order of the bits in each row of the bin_nums array to obtain the correct binary representation.

print(bin_nums[:,::-1]): Prints the resulting array containing the binary representations of the numbers in “nums” with 8 bits.

For more Practice: Solve these Related Problems:

Write a NumPy program to convert a vector of integers into their binary representations as rows of a matrix using np.binary_repr.
Create a function that maps each integer in an array to an 8-bit binary vector and stacks the results.
Implement a solution that uses vectorized operations to convert a 1D array of integers to a 2D binary array.
Test the conversion on a range of integers and verify that each row in the binary matrix has consistent width.

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