Check if all bits of a number are set in Python

In computers, data is stored in the binary form, which uses the two digits 0 and 1. Each digit in this format is known as a bit.

In this article, we are going to check if all bits of a number are set in Python. A bit is said to be set if the binary representation of every bit is 1.

Let's look at some scenarios to understand this better:

Scenario 1

Input: 3
Binary: 111
Output: True
Explanation: All bits are 1.

Scenario 2

Input: 6
Binary: 110
Output: False
Explanation: Not all bits are 1.

Checking if the Bits are set using Python

To check whether all the bits in a number are set to 1, we can use a mathematical pattern. Such numbers are always of the form 2ⁿ - 1, where n is a positive integer.

This is because subtracting 1 from a power of 2 results in a binary number where all the lower n bits are set to 1. For example:

2^1 - 1 = 1 -> Binary: 0b1
2^2 - 1 = 3 -> Binary: 0b11
2^3- 1 = 7 -> Binary: 0b111

Let's dive into the examples:

Example 1

In the following example, we are going to consider the input as 3 and check whether the bits are set:

def demo(n):
   return n != 0 and ((n + 1) & n) == 0
x = 3
result = demo(x)
print(f"Input: {x}")
print(f"Binary: {bin(x)[2:]}")
print(f"All Bits Set: {result}")

Following is the output of the above program:

Input: 3
Binary: 11
All Bits Set: True

Example 2

Following another example, where we are going to take the input as 6 and check whether the bits are set:

def demo(n):
   return n != 0 and ((n + 1) & n) == 0
x = 6
result = demo(x)
print(f"Input: {x}")
print(f"Binary: {bin(x)[2:]}")
print(f"All Bits Set: {result}")

If we run the above program, it will generate the following output:

Input: 6
Binary: 110
All Bits Set: False

Conclusion

To check if all the bits of a number are set in Python, we can use a simple bit-wise trick (n & (n + 1)) == 0. These work perfectly for numbers like 1, 3, 5, 7, etc., where all bits in their binary form are 1.