Binary Converter

A Binary Converter is a tool that helps convert numbers from one numeral system to another, especially between binary and decimal systems.

What Does a Binary Converter Do?

A Binary Converter is used to convert a number from the binary numeral system (base-2) to other numeral systems such as decimal (base-10), hexadecimal (base-16), or vice versa. This tool is essential for tasks in computing, programming, and digital electronics, where binary data is commonly used.

Binary Converter Formula

The formula for converting a decimal number to binary is:

Binary = (Decimal Number) to the base 2

To convert a decimal number to binary:

1. Divide the decimal number by 2.
2. Write down the remainder (either 0 or 1).
3. Divide the quotient by 2 again and repeat the process until the quotient is 0.
4. The binary number is the remainders read from bottom to top.

Binary Converter Examples

Example 1: Converting Decimal to Binary

Let’s convert the decimal number 13 to binary.

1. Divide 13 by 2 → Quotient = 6, Remainder = 1
2. Divide 6 by 2 → Quotient = 3, Remainder = 0
3. Divide 3 by 2 → Quotient = 1, Remainder = 1
4. Divide 1 by 2 → Quotient = 0, Remainder = 1

Reading the remainders from bottom to top, the binary equivalent of 13 is 1101.

Example 2: Converting Decimal to Binary with Larger Numbers

Let’s convert the decimal number 25 to binary.

1. Divide 25 by 2 → Quotient = 12, Remainder = 1
2. Divide 12 by 2 → Quotient = 6, Remainder = 0
3. Divide 6 by 2 → Quotient = 3, Remainder = 0
4. Divide 3 by 2 → Quotient = 1, Remainder = 1
5. Divide 1 by 2 → Quotient = 0, Remainder = 1

Reading the remainders from bottom to top, the binary equivalent of 25 is 11001.

A Binary Converter is an indispensable tool for simplifying numerical conversions, especially for those involved in programming or digital technology, making binary calculations easier and more accessible.