Understanding Binary and Conversions

Understanding Binary

• Binary is a base-2 number system, using only two digits: 0 and 1.
• These digits represent the smallest unit of data in a computer, called a bit.
• Each bit can represent either a "true" (1) or a "false" (0) state.
• Groups of bits are used to represent larger amounts of data. A group of eight bits is one byte.

Converting between Decimal and Binary

• Decimal is the base-10 number system we use everyday.
• Binary numbers can be converted into decimal numbers.
• Decimal numbers can be converted into binary numbers.
• Conversion methods involve place value. Each position in a binary number represents a power of 2.

Representing Data in Binary

• Numbers: Positive and negative integers are represented using different methods depending on the number of bits available.
• Text: Characters are represented using character sets (like ASCII and Unicode). Each character has a unique binary code.
• Images: Images are composed of pixels. Each pixel is represented by a binary code that determines its color. Color depth determines the number of bits used per pixel.
• Sound: Sound is captured as a continuous wave. Analog to digital converters (ADCs) sample the wave at regular intervals, converting the amplitude at each sample into a binary number.

Binary Operations

• Computers perform calculations using binary arithmetic.
• Key binary operations include:
• Addition
• Subtraction
• AND
• OR
• NOT
• These operations are fundamental to how a computer processes information.

Importance of Binary in Computer Systems

• Binary is the language of computers: computers only understand 0s and 1s.
• All instructions and data that a computer processes are ultimately represented in binary.
• Binary arithmetic is vital to the performance of tasks such as calculations, logic gates, and data comparison.

Common Binary Terms

• Bit: The smallest unit of data in a computer system, representing a 0 or 1.
• Byte: A group of eight bits.
• Nibble: A group of four bits.
• Word: A group of bits that is treated as a unit. The size of a word can vary.
• Data Types: Integers, floating-point, characters, etc., are all represented in binary form.

Applications of Binary

• All digital devices use binary.
• Digital images and audio.
• Digital communication.
• Data storage.
• Network communications.
• High-performance computing.