Binary Translator

A binary converter can convert numbers between the way computers and humans represent numbers. When you enter a value and select a number system, this tool will show its representation in binary, octal, decimal, and hexadecimal simultaneously.

Binary is the language of digital devices. Photos, messages and programs are stored at their most basic level as long strings of two symbols: 0 and 1. Each of these numbers is a bit, and eight bits make up one byte. Because it's difficult to read raw bit strings, converting between different number systems is one of the first skills you'll learn in computer science.

How to read binary code.

The binary system is a number system that is very similar to the decimal number we are already familiar with. In the decimal system each digit represents a power of ten. In the binary system, each digit represents a power of two and counting begins on the right; the rightmost digit being the power of 2 raised to zero.

Let's take the binary number 101010 as an example. We write down the powers of two and add up the corresponding places, taking into account that position 1 is considered.

If we add up all of these positions, we get this: 32 + 8 + 2 = 42. So the binary number 101010 is equivalent to the decimal number 42.

How to convert a decimal number to binary.

To convert it back to decimal, repeatedly divide by 2 and note the remainder. Divide the number by 2 and note the remainder (either 0 or 1), then divide the result again by 2. Continue until the result is 0, then read the remainders from bottom to top.

If you convert 42, the remainders from beginning to end are 0, 1, 0, 1, 0 and 1. If you read these from bottom to top, you get 101010, which is consistent with the result that would be obtained by direct conversion.

Binary, octal, decimal and hexadecimal systems:

In the octal system bits are grouped in threes and in hexadecimal they're grouped in fours, which is why programmers often use those systems as shorthand for long binary numbers. Each digit in hexadecimal represents exactly four bits, so a byte will always be represented by two digits in hexadecimal. Here are the first few values:

Bits and Bytes

A single bit can store either a value of 0 or 1. Eight bits make up one byte and a byte can store 256 different values ranging from 0 to 255. Because of this range, a byte is sufficient to represent basic characters or a color channel.

This rule will soon be expanded. A single 16-bit value covers 2 to the power of 16, or 65,536 different possibilities, which is enough to represent tens of thousands of colors that could be displayed on a screen. With each additional bit, the range doubles.

Binary numbers and text: The connection to ASCII

Computers store characters as numbers. A character set is just a predefined table that assigns each character a code. ASCII, or American Standard Code for Information Interchange, is a classic character set where each character uses one byte.

To convert text to binary numbers, you first need to convert each character into its corresponding ASCII code and then write that code in binary. The uppercase letter A has a code of 65 which is represented as the 8-bit value 01000001. The number sign 0 has a code of 48, so it would be 00110000. The space character has a code of 32, which in binary is 00100000.

So a word is made up of a series of bytes. With the above tool, you can convert each character individually into its code and thus assemble the word in binary form.

Where is binary used?

The entire digital world is based on the binary system. Processor instructions, network packets, file formats and colors on your screen are all essentially encoded in binary. Boolean logic, or the algebra of "true" and "false", assigns a value of 1 to true and 0 to false. This is how circuits make decisions.

A Brief History of the Binary System

The modern binary system was founded by the German mathematician Gottfried Wilhelm Leibniz. He published his work in 1703 called "Explication de l'Arithmetique Binaire", where he showed that any number can be represented using only the values of 0 and 1. His inspiration came from the ancient Chinese book "I Ging" which describes states of disconnection and connection.

This idea is even older. Around 200 BCE the Indian scholar Pingala used a system with two states to represent the rhythms of poetry. The binary system was little known until engineers in the 20th century discovered that the "on" and "off" states of an electric switch corresponded perfectly to the values 0 and 1. This led to the digital computer.