Binary Calculator

Binary Calculator makes it easy to perform arithmetic operations with binary numbers. It guides you through binary addition, subtraction, multiplication, and division calculations. This tool performs calculations using both signed and unsigned number formats.

What are Binary Arithmetic Operations?

Binary numbers use base 2 and contain only the digits 0 and 1. They are sequences of bits that represent two possible states: on or off.

Because we usually learn arithmetic using the decimal system, binary arithmetic can seem difficult at first. However, once you understand the basics, it becomes easy! Binary numbers also allow for unique operations, such as bitwise manipulations – AND, OR, XOR – and bit shifts, which are specific to this number system.

What is a binary number?

A binary number represents a value using the binary system, a positional number system with base 2. This system relies on just two digits – 0 and 1 – to express every possible number. For example, the decimal number 10 becomes 1010 in binary, 100 converts to 1100100, and 1,000 converts to 1111101000 in binary. Binary values ​​can also include signs, just like decimal numbers. For example, -101 in binary is equal to -5 in decimal. Currently, the binary calculator or converter mentioned above does not support negative binary values.

People in ancient civilizations such as Egypt, China, and India used binary concepts long ago. However, since the 20th century, binary numbers have become essential to modern computing. Computer architects, programmers, and software developers rely on binary because computer hardware operates using electrical signals that turn on or off. At the most basic level, computers store and process all data using only ones and zeros. Fortunately, most people don’t need to manually calculate in binary, but converters and calculators often come in handy during programming tasks.

With our binary calculator, you can easily perform arithmetic operations such as addition, subtraction, multiplication, and division on binary numbers. You can also use it as a binary converter to convert values ​​between binary and decimal, decimal and binary, hexadecimal and binary, and binary and hexadecimal formats.

Below is a table showing selected numbers written in decimal, hexadecimal, and binary formats (base 10, base 16, and base 2).

How to Use a Binary Calculator for Math Problems

A binary calculator is a tool designed to work efficiently with binary numbers. It helps in quickly performing addition, subtraction, multiplication, and division of binary numbers. A binary calculator includes eleven main operations, which allow users to apply logic functions to given numbers or digits. This calculator displays results not only in binary but also in decimal and hexadecimal formats.

According to Mathematics and Digital Electronics, binary numbers are expressed in the base-2 numeral system, also called the binary system. The binary system has only two digits: “0” (off state) and “1” (on state). Being a positional system with a radix of 2, each single digit is called a bit.

When discussing binary numbers, we refer to each digit individually. For example, the binary number “1112” is read as “one one one two.” Understanding binary numbers prevents confusion with decimal numbers. Each individual digit, such as 0 or 1, is a bit. For example, 1110101 has seven bits.

Binary Addition Calculator

The binary system works similarly to the decimal system, which is the most common in everyday calculations. The decimal system uses the digits 0 through 9, making it a base-10 number system. In contrast, the binary system uses only 0 and 1, making it a base-2 system.

In binary arithmetic, the digits 0 and 1 are called bits. We apply all the standard arithmetic operations – addition, subtraction, multiplication and division – following the same rules as the decimal system.

Binary Subtraction Calculator with Steps

Binary subtraction works like addition but with only two digits. When subtracting, if the number being removed is greater than the number being added, then borrowing occurs.

In binary subtraction, borrowing occurs only when subtracting 1 from 0. Here, 0 in the “borrow” column becomes 2, and 1 in the borrow column is reduced by 1. If the next column also contains 0, then subtraction continues column by column until the subtraction is complete.

Binary Division

Binary division works like decimal division but uses only binary numbers. The dividend is divided equally by the divisor, and subtraction is handled in binary format. Understanding binary subtraction is essential to performing binary division correctly. Consider an example to help you follow the steps clearly.

Binary Subtraction

You can perform binary subtraction using two main methods:

The Borrow method, which works like standard decimal subtraction.

The Complement method, where you replace the subtrahend with its two’s complement and then perform the binary addition.

0 − 0 = 0
0 − 1 = 1 (borrow 1 from the next bit)
1 − 0 = 1
1 − 1 = 0

Binary Multiplication

Binary multiplication looks like decimal long multiplication but is simpler because it only involves 0 and 1. It relies on repeated binary addition. Here are the basic rules, which don’t require any carry:

0 × 0 = 0
0 × 1 = 0
1 × 0 = 0
1 × 1 = 1

How to Use a Binary Calculator?

Now that you understand binary addition, subtraction, multiplication, and division, you know that these operations can get confusing for large binary numbers. That’s where a binary calculator comes in! For example, you can subtract the binary form of 38 from 115. To switch between decimal and binary numbers, use our binary converter.
To add binary numbers with the Binary Math Calculator, follow these steps:

First, select the binary representation you want to work with. If you want, you can select “Other” from the Binary Representation drop-down menu to enter a custom binary format.

Next, type the first number in the top field of the Binary Addition Calculator. Be sure to enter only zeros and ones. You don’t need to include the leading zero; for example, instead of typing “00001111”, just type “1111”.

Then, type the second binary number in the second field.

The calculator will display the results in a table under the Results section.

If you want to see the full equation process, you can also check the Display Long Sum Equation box, and tick the Show Carry Bits option for a full reference to the carry values. Keep in mind, the calculator can only handle binary inputs up to 16 bits due to space limitations.

FAQs: Frequently Asked Questions