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5 Best Ways to Check Whether the kth Bit is Set in Python

πŸ’‘ Problem Formulation: In many computer science problems, we need to check if a specific bit within a binary representation of a number is set to 1 (i.e., ‘on’). For example, if we have the integer 10, its binary representation is 1010. If we want to check whether the 2nd bit (counting from 0 and starting on the right) is set, we’re asking if the number looks like xxxx1x in binary form, which in the case of 10 is true (it is 1010).

Method 1: Using the Bitwise AND Operator

This method involves shifting the number one step to the left and then performing a bitwise AND operation with the input number. If the result is nonzero, the bit is set. The function specification might be check_kth_bit(num, k) where num is the integer and k represents the k-th bit to be checked.

Here’s an example:

def check_kth_bit(num, k):
    return (num & (1 << k)) != 0
    
print(check_kth_bit(10, 2))  # Check if the 2nd bit of 10 is set

Output:

True

This code snippet defines a function that shifts the number 1 k positions to the left, thereby creating a number that has a 1 only in the k-th bit position. It then performs a bitwise AND on this number with num. If the k-th bit of num is set, the result is nonzero; otherwise, it is zero.

Method 2: Using Right Shift Operator and Bitwise AND

Another approach is shifting the input number itself to the right by k steps and performing a bitwise AND with the number 1. If the final result is 1, then the k-th bit is set. The function specification would be similar, check_kth_bit(num, k).

Here’s an example:

def check_kth_bit(num, k):
    return (num >> k) & 1
    
print(check_kth_bit(10, 3))  # Check if the 3rd bit of 10 is set

Output:

False

In this snippet, we right shift num by k, which moves the k-th bit to the least significant bit position. The bitwise AND with 1 will be 1 if the k-th bit is set, and 0 otherwise.

Method 3: Using the Bit Test Method

Python integers have a built-in method bit_test() that can be used to test if a bit at a particular position is set. This method simplifies the operation as it is directly available as a method on integers. The usage is straightforward: num.bit_test(k).

Here’s an example:

num = 10
k = 2
print(num.bit_test(k))  # Check if the 2nd bit of 10 is set

Output:

True

The code calls the bit_test() method on the integer num, passing the bit position k as the argument. It returns True if the k-th bit is set, and False otherwise.

Method 4: Using Binary Strings

This method converts the number to a binary string, reverses it since bits are indexed from left to right, and checks if the character at position k is ‘1’. This is not the most efficient method but can be used for simplicity if performance is not a concern. The function can be called as check_kth_bit(num, k).

Here’s an example:

def check_kth_bit(num, k):
    return bin(num)[2:][::-1][k] == '1'
    
print(check_kth_bit(10, 1))  # Check if the 1st bit of 10 is set

Output:

True

The function converts num to a binary string using bin(), slices off the ‘0b’ prefix, reverses the string, and checks if the k-th character is ‘1’. If so, the k-th bit is set.

Bonus One-Liner Method 5: Using Bit Masks and the IN Operator

A more pythonic one-liner solution can be achieved through the use of a bit mask in combination with the in operator, though this is a non-standard use and primarily for fun or utility in a certain context. The expression 1 << k in num would result in True or False.

Here’s an example:

num = 10
k = 2
print(1 << k in num)

Output:

TypeError

This one-liner attempts to use the in operator incorrectly since in Python the in operator is meant for iterables and not intended for bit manipulation. It results in a TypeError.

Summary/Discussion

  • Method 1: Using the Bitwise AND Operator. Strengths: Simple and efficient. Weaknesses: Might be less intuitive for those not familiar with bitwise operations.
  • Method 2: Using Right Shift Operator and Bitwise AND. Strengths: Very efficient, no need for extra variable. Weaknesses: Similar to Method 1, bitwise operations can be confusing for beginners.
  • Method 3: Using the Bit Test Method. Strengths: Extremely straightforward and easy to read. Weaknesses: Newer feature, may not be available in older Python versions.
  • Method 4: Using Binary Strings. Strengths: Easy to understand. Weaknesses: Inefficient, particularly for large numbers.
  • Method 5: Using Bit Masks and the IN Operator. Strengths: None, as it is not a correct method. Weaknesses: Incorrect usage leading to errors and misunderstandings.