How To Calculate Two’s Complement In Binary Mathematics?

Logical mathematics is as simple as cutting a piece of cake. If you are struggling with getting command over logical calculations, stop worrying. This article is enough to comprehend one of the most used binary maths techniques. This is the two’s complement that we are discussing. We will let you know how you can calculate it either manually or by using the advanced two’s complement calculator. 

What Is Two’s Complement?

In logical mathematics

“The conversion of a positive binary number into a negative binary number that has the same equivalent value in a decimal, octal, or hexadecimal system is known as the two’s complement”

How To Convert a Binary Number To Two’s Complement?

Converting a binary number to its corresponding complement form is fast and accurate if you do it using the two’s complement calculator online. But as a mathematician, you must know how to carry on manual calculations. The process basically consists of a couple of steps which are

  • To invert all the binary bits in a binary number
  • Adding 1 to the least significant bit of the number

So let’s discuss these through examples!



Convert the number 102 into two’s complement form with the steps shown.


Here the given number is 102, which is in its decimal form. First, we need to convert it to its equivalent binary form.

102 in Decimal = 1100110 in binary



The required binary number is as (1100110)2

The free two’s complement calculator can also instantly convert any decimal number to its binary notation before calculating two’s complement form.

Inverting all the bits now 


Adding 1 to the least significant bit of the inverted binary number as follows


+       (1)2




Which is the required answer and can also be checked by 2’s complement calculator. 


Convert the number (1245)10 to its two’s complement form.


We have the number as


The equivalent binary number to this decimal number is


Now converting the binary number to its inverted form as follows


Now in the final step, we will again add 1 to the least significant bit


+                    (1)2




Characterization of Two’s Complement Number

A binary number in two’s complement form is characterized by the following points

  • In a standard two’s complement, a fixed number of bits are used which are 4 by default. But you can also get results for even greater numbers if you use the two’s complement calculator by
  • The bit on the left side is called the most significant bit


In binary number 1010010, the bolded 1 is the most significant bit.

  • You can easily represent any positive and negative equivalent binary numbers with two’s complement notation
  • Using a 4-bit standard notation, you can represent only a couple of numbers in their two’s complement notation. These numbers are 7 and -8 being positive and negative, respectively

Overflow Detection In 2’s Complement

We frequently have a finite amount of bits available when working with binary digits. The system normally only permits a certain amount of bits. As a result, we must be watchful in case there is an overflow.

The majority of overflow cases involve adding two binary values. If the sign bits of the two integers being added match, there will be an overflow. And the outcome has a little the opposite sign. 

For example, adding two positive integers results in a negative result.

Let’s Cover Up Things!

In the following read, we have covered all basics of two’s complement notation. Also, we have enlightened the use of two’s complement calculator in getting swift results during 2’s complement calculations. We hope you may benefit from the article.

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