What is two's complement?

Two's complement is a mathematical operation used to represent signed integers in binary. It is the most common method for representing positive and negative numbers in computer systems, allowing for straightforward arithmetic operations.

How do I use this calculator?

Enter a signed integer (positive or negative) and choose a bit width (e.g., 8, 16, 32). The calculator will compute the two's complement representation and display the result in binary and decimal.

What is the range of values for a given bit width?

For an n-bit two's complement representation, the range is from -2^(n-1) to 2^(n-1)-1. For example, with 8 bits, the range is -128 to 127. The calculator will indicate if the input is out of range.

Math

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Two's Complement Calculator.

Encode a signed integer as fixed-width two's-complement binary.

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Set your values

Results update as you type.

02 / ANSWER

Signed integer

Bit width

Binary

11010110

Unsigned value

214

Results update automatically as you type.

Use Cases

Computer Science Education

Helps students and educators understand how signed integers are represented in binary and how two's complement works.

Example: Convert -5 to an 8-bit two's complement binary number.

Programming and Debugging

Assists programmers in verifying binary representations of integers, especially when dealing with bitwise operations or low-level data.

Example: Check the two's complement of -128 in a 16-bit system.

Frequently Asked Questions

What is two's complement?: Two's complement is a mathematical operation used to represent signed integers in binary. It is the most common method for representing positive and negative numbers in computer systems, allowing for straightforward arithmetic operations.
How do I use this calculator?: Enter a signed integer (positive or negative) and choose a bit width (e.g., 8, 16, 32). The calculator will compute the two's complement representation and display the result in binary and decimal.
What is the range of values for a given bit width?: For an n-bit two's complement representation, the range is from -2^(n-1) to 2^(n-1)-1. For example, with 8 bits, the range is -128 to 127. The calculator will indicate if the input is out of range.

Tips & Common Mistakes

Tips

Ensure the bit width is sufficient to represent the signed integer; otherwise, the result may be incorrect or out of range.
For positive numbers, the two's complement is the same as the standard binary representation.
For negative numbers, the two's complement is obtained by inverting all bits and adding 1.
Use the calculator to verify your manual calculations or to quickly convert between decimal and binary.

Common Mistakes to Avoid

Forgetting to specify the bit width, which can lead to ambiguous or incorrect results.
Assuming that the two's complement of a positive number is different from its binary representation.
Misinterpreting the binary output as unsigned when it represents a signed value.

Last updated: August 13, 2026