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Binary number

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The binary number system is a method of representing numbers using only two symbols, typically 0 and 1. This system was explored by scholars such as Thomas Harriot and Gottfried Leibniz in the 16th and 17th centuries, but instances of binary-like systems have been traced back to ancient Egypt, China, and India. The binary system is fundamental to various arithmetic operations including addition, subtraction, multiplication, and division. Representation and counting in binary systems involve sequences of bits. These sequences can also undergo mathematical operations, with specific procedures for multiplication, long division, and square root calculation. The binary system is critically important in computer[3] science and digital electronics, providing a simpler and more efficient alternative to decimal arithmetic. It forms the basis of computer programming[1] and is vital for digital media[2], internet[4] protocols, encryption, cybersecurity, and precise data storage and manipulation.

Terms definitions
1. computer programming. Computer programming is a crucial field within computer science, which involves the creation of instruction sets that computers execute to accomplish specific tasks. Originating with pioneers like Ada Lovelace, programming has evolved significantly over time. From primitive programmable devices in the 9th century to the advent of stored-program computers in the 1949, the discipline has seen tremendous growth. Various programming languages and tools, like machine code, assembly languages, and high-level languages, have been developed to simplify the coding process. Modern programming places emphasis on quality attributes such as reliability, robustness, usability, portability, and maintainability. It involves various concepts and techniques like readability of source code, algorithmic complexity, and software development methodologies. Besides coding, a programmer's skills encompass prototyping, debugging, documentation, and integration. The field also extends to related topics like computer networking and competitive programming. This discipline is not just about writing code, but understanding and building functional and efficient software systems.
2. digital media. Digital media refers to any form of media that uses electronic devices for distribution. This form of media can be created, viewed, modified, and distributed on digital electronics devices. Digital media encompasses a wide range of items including software, digital images, digital videos, video games, web pages, and websites. It came to prominence with the rise of digital computers which enabled the binary representation of data. Over the years, digital media has evolved, causing significant societal and cultural shifts. It has also impacted various industries such as journalism, publishing, education, and entertainment. Additionally, digital media has given rise to new trends and legal challenges, especially in terms of copyright laws. The consumption of digital media has rapidly increased with growing internet access and the rise of social media platforms.
Binary number (Wikipedia)

A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" (one).

The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit, or binary digit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices, as a preferred system of use, over various other human techniques of communication, because of the simplicity of the language and the noise immunity in physical implementation.

Negative numbers are commonly represented in binary using two's complement.

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