Toggle the First and Last Bits of a Number in C++

13 May 2025 | 4 min read

Given a number n, flip the numbers so that the first and last bits of the binary expansion of the new number are the same; that is, if the bit that was originally assigned is 1, the flipped bit should be assigned 0, etc. It is necessary to leave the elements in between the first and last bits unchanged. Bitwise operators can be applied to work with individual bits in binary quantities or bit patterns.

For Example:

Input = 12

Output = 3

Explanation:

12 -> Binary Expansion of input 12 is 1100

After toggling the first and last bit of binary number 12, it becomes 0011.

0011 à 3

Hence, on toggling the first and last bits of the given input, the output will be 3.

Input = 30

Output = 15

Explanation:

30 -> Binary Expansion of input 30 is 11110.

After toggling the first and last bit of binary number 30, it becomes 01111.

01111à 15

Hence, on toggling the first and last bits of the given input, the output will be 15.

Input = 145

Output = 16

Explanation:

145 -> Binary Expansion of input 145 10010001

After toggling the first and last bit of binary number 145, it becomes 00010000.

00010000 à 16

Hence, on toggling the first and last bits of the given input, the output will be 16.

Approach:

This method uses the left shift operator and bitwise XOR. The bitwise XOR operator evaluates to 1 if the corresponding bit of both operands are different, and evaluates to 0 otherwise. We'll make use of the bitwise XOR operator's bit-toggling functionality. For example, if the integer n has a first bit of 1, n ^ 1 will result in a first bit of 0. Furthermore, the operation n ^ 1 will alter the number's initial bit from 0 to 1 if it is currently set to 0.

We compute n ^ 1 to flip the first bit of the number n. In order to invert the value, it does an XOR operation between the Least Significant Bit and the first bit of n with 1. We create a number, k, in which just the last bit is set, use that number to flip the last bit. The final bit, r, has a location equal to log2(n). It is because the binary expansion of n uses log2(n) bits.

Algorithm:

First, read the input value, n.
Apply XOR to toggle the first bit of n: n = n XOR 1.
Put the value 0 in the counter variable pos.
Assign the value of n to the temporary variable temp.
When the temperature is not zero: Move the temperature to the right by 1%.
- Increase pos by 1.
Apply the XOR operation with a mask to toggle the final bit of n: n = n XOR (1 \\ (pos - 1)).
Give the resultant number, n, out.

Example 1:

Let us take a C++ program to toggle the first and last bits of a number using XOR:

Output:

Toggle the First and Last Bits of a Number in C++

Explanation:

The toggle_first_bit() function toggles the first bit of the number using the XOR operation.
toggle_last_bit() function finds the last digit position and toggles it using XOR.
In the 'main' function, we will call both the functions toggle_first_bit and toggle_first_bit functions to toggle the first and last bits of the input number respectively.
Finally, we will print the decimal value of the modified number as an output.

Complexity Analysis:

Time Complexity:

Its time complexity is O(1) because the method operates in a fixed amount of time regardless of the quantity of inputs.

Space Complexity:

Its space complexity is O(1) because no auxiliary space is utilized in the implementation.

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Toggle the First and Last Bits of a Number in C++

Approach:

Algorithm:

Example 1:

Explanation:

Complexity Analysis:

Time Complexity:

Space Complexity:

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