how to calculate bitwise or of a range of numbers

Rose Montero

2 min read

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08-09-2024

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Calculating the bitwise OR of a range of numbers can seem daunting at first, but it’s a straightforward process once you break it down. This guide will walk you through the steps, using clear examples and analogies to help you understand the concept of bitwise operations.

What is Bitwise OR?

Bitwise OR is an operation that takes two binary numbers and performs the OR operation on each pair of corresponding bits. The result is 1 if at least one of the bits is 1; otherwise, it’s 0.

For example:

• 1101 (binary for 13)
• 1011 (binary for 11)
• Performing OR:
  • 1 OR 1 = 1
  • 1 OR 0 = 1
  • 0 OR 1 = 1
  • 1 OR 1 = 1

So, the result of 1101 OR 1011 is 1111 (binary for 15).

Steps to Calculate Bitwise OR of a Range

Let’s say you want to calculate the bitwise OR of all numbers in the range from a to b. Here’s how you can do it:

Step 1: Initialize the Result

Start by initializing a variable, say result, to zero. This variable will store the cumulative OR of the numbers in the range.

result = 0

Step 2: Loop Through the Range

Create a loop that goes through all the numbers from a to b, inclusive. For each number in this range, perform the bitwise OR with the result variable.

Step 3: Return the Result

Once the loop is complete, the result will contain the bitwise OR of all numbers from a to b.

Example Code

Here's a simple Python code snippet that demonstrates this process:

def bitwise_or_range(a, b):
    result = 0
    for number in range(a, b + 1):
        result |= number  # Bitwise OR operation
    return result

# Example usage:
print(bitwise_or_range(5, 7))  # Output will be 7

Understanding Through Example

Let’s walk through an example using the range from 5 to 7.

• Binary representations:
  • 5 = 101
  • 6 = 110
  • 7 = 111

Now, calculate the OR step-by-step:

• Start with result = 0 (000 in binary)

1. result = 0 | 5 → 000 OR 101 = 101 (5)
2. result = 5 | 6 → 101 OR 110 = 111 (7)
3. result = 7 | 7 → 111 OR 111 = 111 (7)

So, the final result of bitwise OR for numbers between 5 and 7 is 7.

Conclusion

Calculating the bitwise OR of a range of numbers can be easily accomplished through a simple loop and accumulation of the OR results. The operation itself is efficient, making it useful in various programming contexts, especially when dealing with sets of numbers in competitive programming or bit manipulation tasks.

Feel free to explore and try out different ranges and numbers to see how the bitwise OR operation behaves. Happy coding!

Further Reading

• Understanding Bitwise Operations
• Python Bitwise Operators
• Advanced Bit Manipulation Techniques