Binary is a number system that uses two numerals to represent all real numbers. While the most common counting system, the decimal system, uses ten numerals, the binary system uses only 0 and 1.

The binary number system uses only two numbers, 1 and 0.

Each digit in a binary number system therefore represents a power of two. The first digit on the right represents the 0th power, the second represents the 1st power, the third represents the 2nd power, and so on. Therefore, the number 1 in the decimal system is also represented as 1 in the binary system. Number 23, on the other hand, is represented as 10111 (16 + 0 + 4 + 2 + 1).

In a general sense, binary systems can be anything that offers only two options, not necessarily limited to number systems.

The decimal system makes perfect sense to be used by humans. We have ten fingers and ten feet, so when the first humans started counting things, they turned to these readily available markers. Later, when counting systems were codified, it was natural to convert the already used decimal system into a representational system. The binary is also a very natural system, however, since many things “are” or “are not”. Many spiritualist traditions, such as the Pythagoreans and some Indian mystics, made use of this system, therefore, from the 6th century BC.

In 1854, a pivotal paper on binary systems was published by mathematician George Boole. This article laid the groundwork for what would come to be called Boolean algebra. With the advent of electronics, these systems suddenly made incredible sense. Most electronic systems work on a switch-based system, whether the current is running or not. In 1937, Claude Shannon laid the foundation for the theory of circuit design using binary arithmetic. In 1940, the era of binary computing began with the launch of the Bell Labs Complex Number Computer, which was capable of performing extremely complex mathematical calculations using this type of system.

In a more general sense, binary systems can be anything that offers only two options, not necessarily limited to number systems. In the case of electronic switches, for example, the system consists of current-no current. A true-false exam is another example. Yes-no questions are also binary in nature.

There are mathematical methods for converting binary numbers to decimal numbers and vice versa. There are also mathematical devices to perform functions such as addition, subtraction, multiplication and division in different base systems, including binary ones. While converting to or from decimal is a bit of a pain, converting between binary and octal or hexadecimal systems, base eight and base 16 respectively, is much easier. This is because eight and 16 are powers of two, making them integrate well with binary systems. It is for this reason that both octal and hexadecimal are basic systems widely used in computer applications.