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