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Bitwise Negation Calculator

Reviewed by Calculator Editorial Team

Bitwise negation, also known as the NOT operation, is a fundamental operation in digital logic and computer programming. It flips all the bits of a number, converting 0s to 1s and 1s to 0s. This operation is essential for various bit manipulation tasks in programming and digital circuit design.

What is Bitwise Negation?

Bitwise negation is an operation that inverts the bits of a binary number. In other words, it changes every 0 to 1 and every 1 to 0. This operation is represented by the tilde symbol (~) in many programming languages.

The result of a bitwise negation operation is known as the one's complement of the original number. This operation is different from arithmetic negation, which changes the sign of a number.

Key Points

  • Bitwise negation flips all bits of a number
  • It's represented by the ~ symbol in programming
  • The result is called the one's complement
  • It's different from arithmetic negation (-x)

How to Calculate Bitwise Negation

Calculating bitwise negation involves these steps:

  1. Convert the number to its binary representation
  2. Flip all the bits (0s become 1s and 1s become 0s)
  3. Convert the resulting binary number back to decimal

For example, to calculate the bitwise negation of 5:

  1. Binary of 5 is 00000101 (assuming 8-bit representation)
  2. Flipping the bits gives 11111010
  3. 11111010 in decimal is 250

So, the bitwise negation of 5 is 250.

Bitwise Negation Formula

The bitwise negation of a number x can be calculated using the following formula:

Bitwise Negation Formula

~x = (2n - 1) - x

Where:

  • x is the original number
  • n is the number of bits in the representation
  • 2n - 1 is the maximum value that can be represented with n bits

This formula works because it calculates the one's complement by subtracting the original number from the maximum value that can be represented with n bits.

Bitwise Negation Examples

Here are some examples of bitwise negation calculations:

Number (Decimal) Binary (8-bit) Negated Binary Negated Number (Decimal)
5 00000101 11111010 250
10 00001010 11110101 245
20 00010100 11101011 235
30 00011110 11100001 225

These examples show how the bitwise negation operation works for different numbers. Notice that the negated value is always the maximum value that can be represented with 8 bits (255) minus the original number.

Bitwise Negation in Programming

In programming languages like C, C++, Java, and Python, bitwise negation is performed using the tilde symbol (~). Here's how it works in different languages:

C/C++ Example

int x = 5;
int negated = ~x;  // Result: 250 (assuming 32-bit integers)

Java Example

int x = 5;
int negated = ~x;  // Result: 250 (assuming 32-bit integers)

Python Example

x = 5
negated = ~x  # Result: 250 (assuming 32-bit integers)

In all these languages, the bitwise negation operation flips all the bits of the number, resulting in the one's complement.

FAQ

What is the difference between bitwise negation and arithmetic negation?

Bitwise negation flips all the bits of a number, while arithmetic negation changes the sign of a number. For example, the bitwise negation of 5 is 250, while the arithmetic negation of 5 is -5.

How does bitwise negation work with negative numbers?

Bitwise negation works the same way for negative numbers as it does for positive numbers. The operation flips all the bits of the number, regardless of its sign. For example, the bitwise negation of -5 is 4 in 4-bit representation.

What is the one's complement of a number?

The one's complement of a number is the result of flipping all its bits. It's what you get when you perform a bitwise negation operation on the number.

Can bitwise negation be used to find the complement of a number?

Yes, bitwise negation can be used to find the one's complement of a number. The one's complement is simply the result of flipping all the bits of the number.