Welcome to the one's complement calculator (or 1's complement calculator). This tool helps you find the negative equivalent of each positive binary number and shows you how to convert from decimal to one's complement. You will learn how to convert negative decimal values to binary and how to calculate the one's complement.

What are binary numbers?

To understand the binary number system, let's compare it to the decimal system, the numeral system we use in our everyday lives.

  • In the decimal system, numbers are made up of the digits 0 to 9. The system has the base 10, meaning that every digit in the number represents a certain power of 10. The decimal number 123 can be expressed as 1*10² + 2*10¹ + 3*10⁰, using scientific notation.

  • In the binary system, only the digits 0 and 1 are used. Each digit can be understood as a logical state, 0 or 1, yes or no, on or off, and represents a power of the base 2. The binary number 101 can be expressed as 1*2² + 0*2¹+ 1*2⁰.

But this binary representation leaves many problems that we can easily solve for the decimal system: if we can only use the digits 0 and 1, how do we express negative numbers in the binary system? How do we add and subtract binary numbers?

How to convert negative decimal values to binary – the one's complement method.

Before we can use the 1's complement calculator, we have to understand how calculating the one's complement helps us convert negative decimal values to binary.

There are several methods for expressing negative binary numbers, but they all have one basic idea in common: they use the first, the so-called most significant bit, as the signed bit. A 0 on this bit indicates a positive number, a 1 a negative number. Using the first bit as a signed bit, of course, changes the range of numbers expressed with a certain number of bits. While an unsigned 8-bit number ranges from 0 to 255, a signed 8-bit number can express the range -128 to 127.

  • The most intuitive approach is to create a negative binary number by simply flipping the first bit on the positive equivalent. So, since the decimal number 3 is 0011, -3 is 1011. Unfortunately, this approach does not stand the basic test of adding 3 and -3 since the result would be 1110, which is certainly not 0.

  • This 1's complement calculator uses the one's complement method to calculate negative binary numbers. This method states that to determine a negative binary number, you take the positive equivalent, flip the signed bit, and then flip all other bits. So while 3 is still 0011, -3 is now 1100. The addition would now result in 1000, which is better but still not perfect.

  • The two's complement method solves the addition issue to satisfaction. Find more about this topic in our two's complement calculator.

How to use the one's complement calculator?

Now that we know how to calculate the one's complement, let's look at how to use the calculator. In this example, we will find the one's complement for the decimal value 87.

  1. Choose the number of bits. For our example, 8 bits are a good choice since they allow for a range from -128 to 127.

  2. Enter your decimal value in the input field in the decimal to binary section. The calculator displays our number 87 and its binary representation 0101 0111.

  3. The calculator presents you the result: 1010 1000. As we can see, this complies with the formerly described method, flipping the first signed bit to indicate a negative number and all the other bits to achieve the one's complement.

Convert one's complement to decimal.

The one's complement calculator can not only convert decimal to one's complement, but also one's complement to decimal. So let us find the decimal value for the one's complement 1011 1001.

  1. Choose the number of bits. Since our binary number has 8 digits, we choose 8 bit.

  2. Enter your one's complement value in the input field in the binary to decimal section. The calculator displays our binary value and its complement 0100 0110, which is achieved by flipping all bits for the binary input value.

  3. The calculator presents you the result: -70.

Philip Maus
Binary number representation
Decimal to binary
You can enter a decimal number between -128 and 127.
Binary to decimal
You can write a binary number with no more than 8 digits. You don't have to input leading zeros.
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