In digital logic design, the complement is the logical procedure with the help of which you can transform a positive logical number into a negative logical number having the same decimal value. The calculations for the twos complement is done by using the binary number or digit with the longest place value. The major application of the ones or twos complements is seen in the field of computer science. These binary notations are used to type in the numbers with positive or negative signs.

Moreover, if you want to learn what pattern of binary digits are run by the computer behind a certain number you type in the computer, you can use the free online two’s complement calculator by calculator-online.net to learn that particular word pattern.

**Two’s Complement Formula**

Basically, two’s complement helps you to perform conversions between positive and negative binary numbers in the binary digit representation. In a two’s complement binary notation, each significant bit is considered the power of two. And when it comes to the most significant bit, it is also the power of two but in the negative edition. The free two’s complement calculator uses the following formula to calculate the two’s complement of the binary number.

w=-a_{N-1}2^{N-1} + \sum_{i=0}^{N-2}a_i2^i

**Steps To Calculate Two’s Complement**

- If you have any decimal number, first convert it to the corresponding binary number
- After this, you first need to determine the one’s complement of the resulting binary number. For this, just invert the complete binary number bit by bit. By doing this, the number you get is actually the one’s complement of the given binary numeral
- Now to calculate the twos complements, add 1 in the ones complement binary numeral
- To get instant calculations, you may better utilize the twos complement calculator

**Twos Complement of Three Digit Number**

Binary number | 1’s complement | 2’s complement |
---|---|---|

000 | 000 (+0) and 111 (−0) | 000 |

001 | 110 | 111 |

010 | 101 | 110 |

011 | 100 | 101 |

100 | 011 | 100 |

101 | 010 | 011 |

110 | 001 | 010 |

111 | 000 | 001 |

**Calculations**

Let us resolve a couple of examples that will clear your concept in more detail!

**Example # 01:**

Determine the twos complement of the given number:

(1000101010)_{2}

**Solution:**

As the given numeral is:

(1000101010)_{2}

Determining the 1’s complement:

1’s Complement=(0111010101)_{2}

Determining 2’s complement:

(0111010101)_{2}

+ (1)_{2}

___________

(0111010110)_{2}

___________

You can also verify the results by using the two’s complement calculator on the calculator online site.

**Example # 02:**

Calculate the twos complement of the following binary number:

(1001010111111011000111)_{2}

**Solution:**

1’s Complement=(0110101000000100111100)_{2}

Adding 1 to the 1’s complement will yield 2’s complement:

2’s Complement=(01101010000001001111001)_{2}

**Example # 03:**

Determine the twos complement of the given number:

(1000110)_{2}

**Solution:**

As the given numeral is:

(1000110)_{2}

Determining the 1’s complement:

1’s Complement=(0111001)_{2}

Determining 2’s complement:

(0111001)_{2}

+ (1)_{2}

___________

(0111010)_{2}

___________

**Using 2’s Complement Calculator**

By using the free online calculator, you can instantly get the 2’s complement of any number you enter in it. Let us guide you on how you can use this free tool:

- First, select the format of the given number that can be either decimal, binary, or hexadecimal
- Now enter the number and select the number of bits in it
- Tap calculate and you are almost done with your work. The tool will instantly display the 2’s complement of the number entered with step-by-step calculations.

**Last Words**

Calculating two’s complement is very necessary if you want to check for numbers that have similar logical values as the original number. So we hope you have gone through the article above and have understood how to calculate two’s complement.

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