Binary сalculator

Unlock the power of binary arithmetic with ease! Our advanced binary value calculator simplifies and swiftly manages all your binary calculations, turning intricate tasks into quick and easy solutions.

Binary calculation - from addition to division


Binary to decimal converter

Decimal to binary converter

The role of the binary number converter

Binary arithmetic operations are the fundamental mathematical processes applied in the binary number system, which consists exclusively of two digits: 0 and 1.
A binary calculator is a tool designed to perform these arithmetic operations on binary numbers. Unlike traditional calculators that work with the decimal system, a binary calculator exclusively processes binary data. It's an essential tool in fields involving digital electronics and computer programming, where binary calculations are frequently required.
Binary numbers form the core of these operations. They represent values using only two symbols: 0 and 1, each digit being a "bit." In binary, the place values are powers of 2, starting from the rightmost digit (2^0) and increasing to the left. This system is fundamental to computer operations and digital systems.
The types of operations a binary calculator can perform are:
Addition: In binary addition, 0 plus 0 or 1 plus 0 yields 0 and 1 respectively, similar to decimal addition. However, 1 plus 1 results in 0, with a 1 carried over to the next left bit.
Subtraction: Binary subtraction follows the principle where 0 minus 0 and 1 minus 1 result in 0, while 1 minus 0 results in 1. Borrowing is required when subtracting 1 from 0.
Multiplication: Binary multiplication is simpler than its decimal counterpart. Multiplying by 1 gives the same number, and by 0 gives 0. The results are then added following the binary addition rules.
Division: Division in binary is similar to decimal division but uses binary numbers. Dividing by 1 leaves the number unchanged, and dividing by 0 is undefined.
Binary calculators are super handy, not just for pros but also for students. In class, they really bring binary arithmetic to life, turning what might seem like dry theory into something you can actually get your hands on. Whether you're troubleshooting a tricky digital circuit or refining a complex computer program, a binary calculator is the go-to gadget you won't want to be without.

Binary addition

Binary number addition is a fundamental operation in the realm of digital electronics and computing. It's essentially the process of adding two binary numbers, which are sequences of 0s and 1s.
Let's break it down:
  1. When you add 0 and 0 in binary, the sum is 0.
  2. If you add 1 to 0, or vice versa, the sum remains 1.
  3. The intriguing part is when you add 1 and 1. Here, the sum in the current column is 0, but crucially, you carry over a 1 to the next column on the left.
This carry-over is a key aspect of addition in binary. It's similar to how you carry over a digit in decimal addition when the sum exceeds 9, but in binary, this happens whenever you hit a sum of 2.
For example, consider adding binary numbers 10111 and 11010. You start from the rightmost digit (the least significant bit) and proceed to the left. As you add, you'll encounter situations where carrying over is necessary.
In this example, you see how the sum in each column is determined and how the carry-over comes into play. Remembering to carry over when you add two 1s is crucial in binary number addition.

Binary subtraction

Binary subtraction is an essential process in digital systems, involving the subtraction of binary numbers. Here's a breakdown of how to do binary subtraction, focusing on its unique aspects due to the binary system's use of only 0s and 1s.
In binary subtraction, the basic rules are:
0 minus 0 gives 0.
1 minus 0 results in 1.
1 minus 1 equals 0.
0 minus 1 is where borrowing comes into play. You borrow 1 from the next column, converting the 0 to 2 (in binary terms), and then do 2 minus 1, which gives 1.
The concept of borrowing is crucial in the subtraction of binary numbers. When you subtract 1 from 0, you borrow from the next column to the left. This borrowing transforms your 0 into a binary 2, after which you proceed with the subtraction. If the next column also contains a 0, continue borrowing from each subsequent column until a column with a 1 is found.
Here are two examples to illustrate subtraction in binary:
Subtracting 1101 from 1111:
In a case involving multiple borrowings, subtracting 11 from 100:
In these examples, borrowing is indicated by the changes in each bit: the borrowing column effectively becomes 2, while the column borrowed from decreases by 1.

Binary multiplication

Binary multiplication is a straightforward process, especially since it only involves 0s and 1s. Here’s how you multiply binary numbers:
0 multiplied by 0 equals 0.
0 multiplied by 1, or 1 multiplied by 0, also equals 0.
1 multiplied by 1 equals 1.
When you multiply binary numbers, you follow a step-by-step process that’s a bit like layering and adding up results. The simplicity of binary digits means each step in the multiplication is either adding the number itself or adding zero.
Let's take an example of multiplying 1011 by 11 in binary:
In this multiplication, for each digit in the second number (starting from the right), you multiply the entire first number. If the digit is 1, you write down the first number. If it’s 0, you write down a row of zeros. Each row is shifted one place to the left as you move to the next digit.
Binary multiplication is all about repeating these simple steps: multiply, shift, and add. It’s a series of straightforward actions that are the core of binary arithmetic.

Binary division

It is an essential operation in digital electronics, involves dividing one binary number (the dividend) by another (the divisor). This process heavily relies on binary subtraction.
Here's a simplified explanation of how the division of binary numbers works:
  1. Arrange the dividend and divisor as in traditional division.
  2. Compare the dividend’s leftmost bits with the divisor. Include more bits if needed.
  3. If the divisor fits, subtract it from the dividend part and write the result below.
  4. Write '1' in the quotient if the divisor fits; otherwise, write '0'.
  5. Repeat until all dividend bits are processed.
For example, dividing 1011 by 11:

Frequently asked questions

What are the rules for adding two binary numbers?

Why use a binary calculator for adding two binary numbers?

How do you add negative binary numbers?