Convert Binary to Decimal -
Convert Decimal to Binary

Convert binary numbers to decimal numbers and vice versa

Binary and Decimal

In the world of computer science and mathematics, there are two commonly used numbering systems: the binary and the decimal system.

The decimal system is a base 10 numbering system, which means it uses ten digits to represent numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. This is the numbering system we use in our daily lives and are most familiar with.

The binary system, on the other hand, is a base 2 numbering system. It uses only two digits to represent numbers: 0 and 1. This system is often used in computers and other electronic systems because these devices process data in a format that is compatible with an on/off switch. This makes the binary system ideal.

Because computers internally use binary numbers, we often have to convert numbers between the decimal and binary system. For example, when a human user inputs a decimal number, the computer must convert this decimal number into a binary form to process it. Conversely, when the computer completes a calculation and produces a binary output, this binary number must be converted into a decimal number to be understandable to the human user.

The conversion between decimal and binary numbers can be done using a few simple algorithms.

Converting from Decimal to Binary

1. Divide the decimal number by 2.
2. Record the remainder.
3. Divide the quotient from the previous step by 2 again.
4. Repeat steps 2 and 3 until the quotient is 0.
5. The binary number is the collection of remainders, read from bottom to top.
    

Converting from Binary to Decimal

1. Start on the right side of the binary number (the least significant digit).
2. For each digit, multiply the digit by 2 to the power of its position (starting from 0 on the right).
3. Add up all these values. This is the decimal equivalent of the binary number.
    

Understanding binary and decimal numbers and how they can be converted into each other is an important part of computer science and computer engineering. This knowledge is also useful in other disciplines, such as electronics, mathematics, and even cryptography.

Conversion table