# One's Complement Calculator

Created by Philip Maus
Reviewed by Steven Wooding
Last updated: Sep 29, 2023

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 $1\cdot10^2 + 2\cdot10^1 + 3\cdot10^0$, 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 $1\cdot2^2 + 0\cdot2^1+ 1\cdot2^0$. The binary converter at Omni Calculator analyzes in depth this topic, don't miss it!

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 calculate the binary addition? And how do we 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.

## 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: $-70$.

Looking for a comprehensive tool for all your binary problems? Our binary calculator will take care of it!

## FAQ

### What is one’s complement?

One's complement is a binary number obtained by flipping all the bits of a given binary number. This operation is used to represent negative numbers in binary. The first bit denotes whether the number is positive (0) or negative (1).

### How do I calculate one's complement?

In order to calculate a the one's complement of a binary number, follow these steps:

1. If converting from a positive, decimal number:
1. Write the initial number in binary.
2. Add an extra 0 at the beginning.
3. Flip all the bits - change all the 1's to 0's and all the 0's to 1's.
2. If you already have a signed binary number, just flip all the bits. Remember, if the initial number starts with a 0, it is negative. If it starts with a 1, it is positive.

### What is one's complement of 7?

One's complement of 7 is 1111 1000, assuming an 8-bit representation. Since the first bit is 1, we know it represents a negative number, in this case, -7.

### What are the disadvantages of one’s complement?

There are several disadvantages to one's complement representation of negative numbers:

1. It requires an extra bit to be reserved for the sign, which leaves us with fewer bits to represent the actual number.
2. Adding two one's complements is not very straightforward. After adding the binary numbers, you might get an end-around carry bit that needs to be added to the last bit.
3. There are two ways to write the number 0 in this notation: 0000 0000 and 1111 1111.
Philip Maus
Binary number representation
8-bit
Decimal to binary
You can enter a decimal number between -128 and 127.
Decimal
Binary to decimal
You can write a binary number with no more than 8 digits. You don't have to input leading zeros.
Binary
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