Binary Calculator

Our binary calculator is a useful tool for calculating binary numbers. It can effortlessly add, subtract, multiply, and divide binary numbers. There are 11 operations that may be performed on the provided integers, including OR, AND, NOT, XOR, and others. It returns results in binary, decimal, and hexadecimal formats.

The binary system

The binary system is a numerical system that works almost identically to the decimal number system that most people are familiar with. While the decimal number system has 10 as its base, the binary number system has 2. Furthermore, while the decimal system employs digits 0 through 9, the binary system employs just digits 0 and 1, with each digit referred to as a bit.

Aside from these distinctions, activities such as addition, subtraction, multiplication, or division are all computed in accordance with the decimal system's principles. Because of the simplicity of implementation in digital circuits utilising logic gates, almost all current technologies and computers employ the binary system.

It is significantly easier to develop circuitry that detects only two states, on and off (or true/false, present/absent, and so on). Using a decimal system would need more complex electronics capable of detecting 10 states for the numbers 0 through 9.

What is a binary number ?

A binary number is a number stated in the binary system, which is a positional numeral system with a base of two that employs just two symbols to represent all conceivable numerical values:

0 and 1. For example, 10 decimal equals 1010 binary, 100 decimal equals 1100100 binary, and 1,000 decimal equals 1111101000 binary.

Binary numbers, like decimal numbers, contain signs; for example, -101 is equal to -5 in decimal. For the time being, the binary calculator / binary converter above does not support negative numbers.

Binary Number calculator

While binary numerals were historically used in Egypt, China, India, and other cultures, they have primarily been used in computing since the twentieth century, primarily by computer system designers, software engineers, and programmers, among others, because the underlying computer systems encode everything with the presence or absence of an electrical charge.

As a result, at the most fundamental level of abstraction, everything in a computer system is represented by ones and zeros. Fortunately, most of us do not need to conduct binary arithmetic or counting, although a calculator or converter may be useful in computer programming.

Our binary calculator allows you to perform arithmetic operations on binary numbers (addition, subtraction, multiplication, and division) as well as use it as a binary converter for binary to decimal, decimal to binary, hex to binary, and binary to hex conversions.

Here's a table with some integers expressed in decimal, hexadecimal, and binary formats (base 10, base 2 and base 16).

Applications of the binary system

Almost all current technologies and computers employ the binary system due to its simplicity in digital circuitry using logic gates. It is significantly easier to create hardware that just requires two states. These two states might be true or false, on or off, and so on.

In a decimal system, on the other hand, it is evident that the hardware design would work on the ten states because the decimal number system is based on the digits 0 to 9.

Converting to and from binary numbers

Converting numbers to and from binary has no effect on the number itself; it only alters its form. You can conduct both sorts of conversions fast and simply using our binary converter above, or you can learn how to do it manually below.

It is important to note that binary computation and binary conversion are distinct operations: you do not need to do one to conduct the other.

Binary to Decimal Calculator

Each binary numeral place represents a power of two, just as each decimal number point represents a power of ten. For example, the decimal representation of the number 20 is 2 x 10¹ + 0 x 10⁰ = 20. In decimal, the binary number 101 is 1 x 2² + 0 x 2¹ + 1 x 2⁰ = 4 + 0 + 1 = 5.

To convert from binary to decimal, take each position and multiply its value by 2 to the power of the position number, counting from right to left and beginning at zero. If you need to compute big exponents like 216, our exponent calculator may come in handy.

Decimal to binary Calculator

Going from a higher base to a lower base is a more complicated operation. This is when having a tool like our binary converter available comes in helpful. Assume the number to be converted from decimal to binary is X.

Begin by determining the greatest power of 2 X and denoting it by E. Then, take note of how many times the power of 16 indicated above goes into X. Y1 represents the remainder.

Repeat the preceding steps with Yn as a beginning value until 2 is more than the remaining value, then assign the remainder to the 20 place, and you will have your hex value.

Decimal to Binary step by step method

To convert a decimal number to a binary number, carefully follow these procedures.

• Find the greatest power of 2 in the given number
• Subtract the value from the given number
• Find the greatest power of 2 within the remainder found in the previous step
• Find the greatest exponent of 2 in the remainder of the previous step
• Repeat the preceding steps until no remainder pops out
• Enter 1 for each identified binary place value and 0 for the remaining values

Converting from binary to decimal is simpler. Determine all 1 places and add the values together.

11110 = (1 × 2⁴) + (1 × 2³) + (1 × 2²) + (1 × 2¹) + (0 × 2⁰)

16 + 8 + 4 + 2 + 0 = 30.

Binary number algebraic operations

You may execute the four fundamental arithmetic operations on binary integers with our tool in binary calculator mode: addition, subtraction, multiplication, and division.

To perform binary calculations on their own, most people would prefer to use a table for lower numbers and a calculator for bigger ones.

Subtraction operates the same as any other number system, with the exception that when borrowing a number, you must borrow a group of 210 rather than 1010 as you would with decimals.

Binary Addition Calculator

Binary Addition Calculator follows the same concepts as decimal addition, but instead of adding a 1 when the applied numbers exceed 10, it adds when the addition results are similar to 2.

Addition Rules in the Binary System

Let’s add two binary numbers to understand the binary addition.

1 1 1 1 + 0 1 0 1 = 1 0 1 0 0

The only major distinction is that the binary number 2 equals 10 in the decimal system. If 1+ 1= 0 also takes 1 from the preceding column to the right, you have made a frequent binary addition error. Instead of 0, the value at the bottom of the transferred number should be 1.

Binary Subtraction Calculator

Except for those resulting from the usage of just numbers 0 and 1, binary subtraction calculator is nearly identical to binary addition. Lending a number occurs whenever the amount removed is larger than the number by which it was deducted.

Borrowing is only suitable in binary subtraction when 1 is subtracted from 0. If this occurs, the 0 in the borrowing column becomes a 2, and the 1 in the borrowing 1 column is lowered. If the next column is likewise 0, borrowings from each column must be carried out in order to decrease a column with a value of 1 to 0. We will discuss the rules.

Rules of Subtraction

Binary Multiplication calculator

Binary multiplication calculator is also not as difficult as it appears. Because the only values utilised are 0 and 1, the numbers to be added are comparable to the first word or 0.

As with decimal multiplication, placeholder0 must be entered in each consecutive section, and the value must be shifted to the left. Binary multiplication may appear complex to you due to the repetitive binary addition, but it is not.

Rules of Multiplication

Binary Division calculator

The binary division calculator procedure is analogous to the long decimal number system division procedure. The divider always divides the payout evenly, and the only significant change is that binary subtraction is used instead of decimal subtraction. Understanding binary subtraction is necessary for understanding binary division.

How to Use our Binary Calculator?

Unlike some other online binary addition or binary multiplication calculators, a binary calculator with answer is incredibly simple to use. Many binary subtraction calculators accessible online have comparable functionality but are extremely difficult to use

This is where our binary operations calculator excels in terms of use as well as accuracy, speed, efficiency, and dependability.

Insert one operand into each input box. Operands should not be written in scientific notation, should be a positive or negative number with no commas or spaces, and should not be expressed as a percentage.

Fractional values are given a radix point, while negative numbers are given a minus sign. For the operands, the input boxes are labelled "First number" and "Second number."

On the provided operands, there are more than 10 operations possible. Addition, subtraction, multiplication, division, AND, OR, NOT, XOR, Left Shift, Right Shift, and Zerofill Right Shift are among these operations. To run the specified operations on the provided binary operands, click the "Calculate" button.