Binary To Decimal Converter

Binary to Decimal Converter

Binary to Decimal Converter is an online tool that helps to convert binary numbers into decimal numbers. 

What is the Binary Number system?

In this system, numbers are used in binary form and it is also based on the 2-number system. It contains the element only “0 and 1” and its domain set can be written as the {0, 1}.

Moreover, Binary number system plays an exclusive role in computer programming and every number in this system is referred to as the bit.

What is a Decimal Number system?

This system is based on the 10 numeral system and contains the number of digits from “0 to 9”. The set of the numbers can be stated as the {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and it plays an important role in our daily life use.  

Steps to Convert Binary to Decimal Number

Follow the below steps to convert the number from binary to decimal.

• First, write the binary number and count the number to move from right to left. Then place the value in the exponent of 2 (power starts from zero) for non-decimal numbers and for decimal numbers power starts from “-1” and so on after the decimal point to move from left to right.
• Write each binary digit with its corresponding power of 2 to move from right to left.
• Solve all powers and add the products.
• Then final answer is the required decimal number.

Example 1:

Convert the “101011” into a Decimal number.

Solution

Step 1: Write the given binary number.

= 101011

Step 2: Place the digit value in the exponent of “2” with the multiple of its digit and simplify.

(101011)₂= (1 × 2⁵) + (0 × 2⁴) + (1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰)

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

Multiply all terms and add them to get the final answer.

                = (32) + (0) + (8) + (0) + (2) + (1)

                = 32 + 0 + 8 + 0 + 2 + 1

                = 32 + 8 + 2 + 1
(101011)2 = (43)10

Example 2:

Convert the given binary number “1011.11” into the decimal number.

Solution

Step 1: Write the given binary number.

= 1011.11

Step 2: Place the digit value in the exponent of “2” with the multiple of its digit and simplify.

(1011.11)₂ =(1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰) + (1 × 2⁻¹) + (1 × 2⁻²)                  

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

Multiply all terms and add them to get the final answer.

                   = (8) + (0) + (2) + (1) + (1/2) + (1/4)

                   = 8 + 0 + 2 + 1 + 0.5 + 0.25

                   = 8 + 2 + 1+ 0.5 + 0.25
(1011.11)2 = (11.75)10