# Binary Complement Calculator Binary and Decimal Conversion, Support for Signed Numbers and Complements

## Binary and Complement Converter Features:

This tool allows conversion of input numbers between binary and decimal. It supports both positive and negative numbers, providing results for both 1's complement and 2's complement, and accepts input of complements to obtain the original binary numbers.

## What are complements?

In the field of computer science, complements are a way to represent negative numbers. The most common complements are 1's complement and 2's complement. The 1's complement is obtained by flipping each digit of a binary number (0 becomes 1, and 1 becomes 0). The 2's complement, based on the 1's complement, involves adding 1. This method is widely used in modern computer systems as it simplifies addition and subtraction operations. For example, suppose we have an 8-bit binary number 10011011; its 1's complement is 01100100, and its 2's complement is 01100101. For more details, refer to Two's complement

## How are complements applied?

In the computer field, using complements to represent and operate with negative numbers has several main advantages:

- Simplified hardware design: Using complements simplifies the hardware implementation of addition and subtraction operations. For example, to calculate A-B, we only need to convert B to its complement and then add A and the complement. This way, the same adder can perform addition and subtraction operations.
- Storage space saving: Using complements allows differentiation between positive and negative numbers in binary representation only at the highest bit (sign bit). Thus, we don't need extra space to store the sign of the number.
- Convenient number comparison: In a complement system, we can directly compare the size of two binary numbers without considering their sign. This is because in a complement system, for any two numbers A and B, if A > B, then the binary representation of A is definitely greater than the binary representation of B.

## Ways in various programming languages to convert decimal to binary

Java | Integer.toBinaryString(decimal_number) |

JavaScript | let binary = decimal_number.toString(2); |

Microsoft .NET / C# | string binary = Convert.ToString(decimal_number, 2); |

Python | binary = bin(decimal_number)[2:] |

Ruby | binary = decimal_number.to_s(2) |

Go | import strconv binary := strconv.FormatInt(decimal_number, 2) |