Binary To Decimal Converter

Binary to Decimal Converter

Binary to Decimal converter converts the binary number into decimal numbers very precisely. It is a very fast and efficient converter that can be used by anyone without any restriction because it is completely free of cost. Arithmetic operations are performed in the form of binary instructions in digital circuits. Therefore in digital electronics & communication, the decimal to binary conversion is more necessary to grasp the processes in a human way.

Binary to decimal conversion is one of the most significant computer and communication operations. This conversion is used for the observation of binary numbers in their corresponding decimal numbers. The best way to understand such operations is to represent a binary in the decimal number system.

How to use our Binary to Decimal Converter?

This binary number converter is a perfect binary to decimal calculator for binary conversion. To convert binary to base 10 or binary to number, this tool comes in very handy because it is available online, and you can make your conversions on the go by using this binary to dec converter.

Making conversions using the above converter doesn't require any prior knowledge of number systems on anything related to them. You just need a binary number or string to convert it to decimal. Enter a binary number into the above input box, or you can load sample data by clicking on the "Load Sample Data" button to get an idea of a binary number. After entering the binary number, press the "Calculate" button.

It will show you the converted number into a decimal number system as soon as you click the 'calculate' button. It will also give you the decimal number from signed 2's complement and a hex number. For your better understanding, this binary to decimal converter also provides the complete process of conversion from binary to decimal by showing the step-by-step calculation on the screen.

How to Convert Binary to Decimal?

A binary number can be converted to a decimal number by using the position method. Converting binary to decimal could be a complicated task depending on the length of a binary string, and that is why the converter above is so useful for making this process a whole lot easier. To convert the binary numbers into decimals, follow these steps.

Step 1: First of all, write down the binary number on the paper that you want to convert into decimal.

Step 2: The bin-to-dec conversion is carried out by starting from the right side of the binary string. Starting from the right, the first digit has position 0, the second has 1, and so on. Multiply each digit by 2 and raise the position of the digit to the power of 2.

Step 3: In this last step, add all numbers after completing the second step, and the result will be a decimal number.

Example:

Convert (1010)₂ to decimal number.

Step 1: Write the binary number (1010)₂ and identify the positions of each digit. Because it is a 4 digit binary number, it will have a total of 3 positions starting from 0.

Step 2: Write each binary digit by multiplying it with base 2 along with its position and add them.

 (1 × 2 ³) + (0 × 2 ²) + (1 × 2 ¹) + (0 × 2 ⁰)

Step 3: Calculate the final value.

(1 × 8) + (0 × 4) + (1 × 2) + (0 × 1) = 8 + 0 + 2 + 0 = 10

So, the binary number (1010)₂ is equal to (10)₁₀ in decimal number system.

Convert (1110010)₂ to decimal

Let's convert (1110010)₂ into a decimal numbers by following the above method.

Step 1: Write the binary number (1110010)₂ and identify the positions of each digit. Because it is a 7 digit binary number, it will have a total of 6 positions starting from 0.

Step 2: Write each binary digit by multiplying it with base 2 along with its position and add them.

(1 × 2 ⁶) + (1 × 2 ⁵) + (1 × 2 ⁴) + (0 × 2 ³) + (0 × 2 ²) + (1 × 2 ¹) + (0 × 2 ⁰)
Step 3: Calculate the final value.

(1 × 64) + (1 × 32) + (1 × 16) + (0 × 8) + (0 × 4) + (1 × 2) + (0 × 1)

= 64 + 32 + 16 + 0 + 0 + 2 + 0 = 114

So, the binary number (1110010)₂ is equal to (114)₁₀ in the decimal number system.

Convert (1001110101)₂ to decimal

To convert this binary number into a decimal, follow the following steps.

Step 1: Write the binary number (1001110101)₂ and identify the positions of each digit. It will have a total of 9 positions starting from 0 because it is a ten-digit binary number.

Step 2: Write each binary digit by multiplying it with base 2 along with its position and add them.

(1 × 2 ⁹) + (0 × 2 ⁸) + (0 × 2 ⁷) + (1 × 2 ⁶) + (1 × 2 ⁵) + (1 × 2 ⁴) + (0 × 2 ³) + (1 × 2 ²) + (0 × 2 ¹) + (1 × 2 ⁰)
Step 3: Calculate the final value.

(1 × 512) + (0 × 256) + (0 × 128) + (1 × 64) + (1 × 32) + (1 × 16) + (0 × 8) + (1 × 4) + (0 × 2) + (1 × 1)

=512 + 0 + 0 + 64 + 32 + 16 + 0 + 4 + 0 + 1 = 629

So, the binary number (1001110101)₂ is equal to (629)₁₀ in the decimal number system.

Binary to Decimal Table

The binary to decimal chart is given below for conversion purposes.