Binary To Decimal

To use this new Binary to Decimal converter tool, type any binary integer like 1011 into the binary number field above, and then click the Convert button. You can get the result in a Decimal number. It is possible to convert up to 63 binary characters to decimal.

Use the RESET button to clear the calculator.

The SWAP button will help you to switch between Binary to Decimal and Decimal to Binary.

Conversion steps:

1. Pick the last integer of the binary number, and call this digit the current digit.
2. Consider a variable ‘power’. Set the value to 0.
3. Multiply the current digit with a 2^power value, and store the result.
4. Increment the power by 1.
5. Set the current digit to the previous digit of the binary number.
6. Follow step 3 until all digits have been multiplied.
7. Add all the results of step 3 to get the decimal number answer.

For Example:

(111100000001)B = (1 × 2¹¹) + (1 × 2¹⁰) + (1 × 2⁹) + (1 × 2⁸) + (0 × 2⁷)
+ (0 × 2⁶) + (0× 2⁵) + (0 × 2⁴) + (0 × 2³) + (0 × 2²) + (0 × 2¹) + (1 × 2⁰)

(111100000001)B = (3841) D

Binary System

Binary is the simplest type of number system that makes use of only two numbers 1 and 0. By using these numbers, arithmetical problems can be solved by machines because, in digital instruments, a transistor is used in two states. Those two states can be represented by 0 (False) and 1 (True). That’s why this number system is the most chosen in modern computer engineering, networking, and communication technologies by specialists, and other professionals.

Decimal System

The decimal number system is also known as the Base 10 numbering system because it is based on 10 ranging symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. In the decimal system, every digit holds its own position along with the decimal point. I.e. the number 326.34 has 4 in the Hundredths position, 3 in the Tenths position, 6 in the Unit position, 2 in the Tens position, and 3 in the Hundreds position.

A Decimal number system is also one of the ancient numeral systems, whose roots are in the Hindu-Arabic numeral system.