Binary number, also known as the base-2 number system, is a system of representing numbers using two symbols or digits. Binary number represents all values by using only two symbols: “0” and “1.” This is different from the decimal or base-10 system, which uses the values 0-9. Binary numbers are commonly used in computers and digital systems because they provide a convenient method of storing and transferring information quickly and efficiently.

In the binary system, each decimal (base 10) number is converted to its binary equivalent. For example, the decimal number 4 becomes 100 because 4 divided by 2 is 2 (with a remainder of 0). To convert a decimal number to its binary equivalent, the number is divided by two repeatedly, and each remainder is featured in the binary representation of the number. So, for example, the number 17 is converted to its binary equivalent, 10001, with the following steps:

17/2 = 8.5 -> Remainder: 1 | 8/2 = 4 -> Remainder: 0 | 4/2 = 2 -> Remainder: 0 | 2/2 = 1 -> Remainder: 0 | 1/2 = .5 -> Remainder: 1

Therefore, the binary equivalent of ’17’ is ‘10001.’

Binary numbers are also commonly used in computer programming. In programming, binary numbers are used as a representation of the on and off states of computers and other digital systems. The ‘1’ in binary numbers is used to represent the on state, while a ‘0’ is used for the off state. This binary system is exploited by computers and digital systems to represent data in a two-state system, such as text, numbers, sound, and images. Binary code is compiled into a language that the computer can understand and execute; this is known as machine code.

Binary code has become an integral part of computer systems, as it is the most efficient way to represent and store data in a digital system. By using the binary system, computers are able to process information quickly and accurately, improving the speed and efficiency of computer systems.