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1's Complement of Negative Number Calculator

Reviewed by Calculator Editorial Team

In digital systems, the 1's complement is a fundamental operation used in binary arithmetic. This calculator helps you find the 1's complement of any negative number, with clear explanations of the process and practical examples.

What is 1's Complement?

The 1's complement of a binary number is obtained by inverting all the bits (changing 0s to 1s and 1s to 0s). This operation is commonly used in computer arithmetic, particularly in the representation of negative numbers in signed binary systems.

In most modern systems, 2's complement is preferred over 1's complement because it simplifies arithmetic operations and avoids the need for an end-around carry. However, 1's complement is still relevant in certain contexts, such as error detection and correction codes.

How to Calculate 1's Complement

To find the 1's complement of a binary number:

  1. Write down the binary number.
  2. Invert each bit (0 becomes 1, 1 becomes 0).
  3. The result is the 1's complement.

Formula: 1's complement of a binary number is obtained by flipping all bits.

1's Complement of Negative Numbers

When working with negative numbers in binary, the 1's complement is calculated by first converting the number to its absolute value, then finding the 1's complement of that value. This is because the 1's complement operation is defined for positive numbers.

For example, to find the 1's complement of -5 in 4-bit binary:

  1. Convert -5 to its absolute value: 5.
  2. Convert 5 to binary: 0101.
  3. Find the 1's complement of 0101: 1010.

The 1's complement of -5 is 1010.

Examples

Let's look at a few examples to illustrate how to calculate the 1's complement of negative numbers.

Example 1: 4-bit 1's Complement of -3

  1. Absolute value of -3: 3.
  2. Binary of 3: 0011.
  3. 1's complement of 0011: 1100.

The 1's complement of -3 is 1100.

Example 2: 8-bit 1's Complement of -10

  1. Absolute value of -10: 10.
  2. Binary of 10: 00001010.
  3. 1's complement of 00001010: 11110101.

The 1's complement of -10 is 11110101.

FAQ

What is the difference between 1's complement and 2's complement?
The main difference is that 2's complement is obtained by adding 1 to the 1's complement. This makes 2's complement more suitable for arithmetic operations because it provides a unique representation for zero and simplifies subtraction.
Can the 1's complement be used to represent negative numbers directly?
Yes, in some systems, the most significant bit (MSB) is used as a sign bit, where 0 represents positive and 1 represents negative. The remaining bits represent the 1's complement of the absolute value.
Is the 1's complement operation reversible?
Yes, applying the 1's complement operation twice returns the original number. This property makes it useful in error detection and correction codes.