Numbers and computers have a close relationship, as computers are designed to process and manipulate numbers in order to perform various tasks and calculations.
Computers use a binary system, which consists of only two digits (0 and 1), to store and process numbers. These digits are represented by electronic switches that are either on (1) or off (0), and can be combined to represent various numbers and operations.
Binary numbers are the foundation of computing, as all data and instructions are ultimately translated into binary code for the computer to understand. They allow for efficient storage and manipulation of data, making modern computing possible.
Real numbers, which include decimal numbers and fractions, are typically represented in computers using floating-point representation. This involves breaking the number into its binary components, including a sign bit, exponent, and mantissa, to allow for a wider range of values and more precise calculations.
Computers have a limited range and precision when it comes to numbers. They can handle a wide range of numbers, including very large and very small numbers, but may encounter errors when dealing with extremely large or infinitely repeating numbers. Additionally, some types of numbers, such as imaginary or irrational numbers, may require special algorithms or programming to be handled by computers.