Binary Calculator

Understanding Binary

The binary system is a base-2 numeral system that uses only two symbols: 0 and 1. It is the foundational language of computers and digital electronics. Each digit in a binary number is called a "bit".

Binary to Decimal Conversion

To convert a binary number to its decimal equivalent, you multiply each binary digit by 2 raised to the power of its position (starting from 0 on the right) and sum the results. For example, the binary number 1101 is converted as follows:

(1 * 2³) + (1 * 2²) + (0 * 2¹) + (1 * 2⁰) = 8 + 4 + 0 + 1 = 13

Decimal to Binary Conversion

To convert a decimal number to binary, you repeatedly divide the decimal number by 2 and record the remainder. The binary result is the sequence of remainders read from bottom to top. For example, to convert the decimal number 13:

• 13 ÷ 2 = 6, remainder 1
• 6 ÷ 2 = 3, remainder 0
• 3 ÷ 2 = 1, remainder 1
• 1 ÷ 2 = 0, remainder 1

Reading the remainders upwards gives the binary number: 1101.