Binary is a number system that uses two numbers to represent all real numbers. While the most common counting system, the decimal system, uses ten numbers, the binary system uses only 0 and 1.
The binary number system uses only two numbers, 1 and 0.
Therefore, each digit in a binary number system represents a power of two. The first digit to the right represents the power of 0, the second represents the power of 1, the third represents the power of 2, and so on. Therefore, the number 1 in the decimal system is also represented as 1 in the binary system. The 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 a lot of sense for humans to use. We have ten fingers and ten feet, so when early 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 representation system. However, binary is also a very natural system, since many things “are” or “are not”. Many spiritualist traditions, such as the Pythagorean and some Indian mystics, made use of this system, therefore, from the sixth century BC
In 1854, the mathematician George Boole published a seminal paper on binary systems. This article laid the foundation 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 circuit design theory using binary arithmetic. In 1940, the era of binary computing began with the release of the complex number computer from Bell Labs, 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-non-current. A true or false test is another example. Yes or no questions are also binary in nature.
There are mathematical methods to convert binary numbers to decimal numbers and vice versa. Mathematical devices also exist 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 tricky, 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, so they integrate well with binary systems. That is why both octal and hexadecimal are basic systems widely used in computer applications.
