Basics of Data Representation

Binary Data

• Binary numbers are base-2 and consist solely of 0s and 1s. Computers use binary due to their on/off nature.
• Bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit.
• Byte: Eight bits combined form one byte. A byte can hold one character of data (e.g., a letter or a number).

Number Systems

• Binary (Base-2): Only two digits, 0 and 1, are used.
• Decimal (Base-10): This system uses ten digits, 0 through 9, and is the most commonly used number system.
• Hexadecimal (Base-16): This system uses sixteen digits. It goes from 0 through 9, then uses 'A' for 10, 'B' for 11, up to 'F' for 15.
• Octal (Base-8): This system uses eight digits, 0 through 7.

Character Encoding Standards

• ASCII (American Standard Code for Information Interchange): it uses 7 or 8 bits, giving it a total of 128 or 256 possible characters.
• Extended ASCII: it's an 8-bit character set derived from the original 7-bit ASCII, allowing for an additional 128 characters.
• Unicode: it can use variable bit encoding and can represent over a million characters, covering all modern languages and many historic ones, symbols, emojis, etc.
• The ord() function in Python takes a single character and returns the Unicode integer value for that character.

Images, Sound and Video

• Bitmap images are represented as a series of dots known as pixels. Each pixel is represented in binary.
• Sound and video are captured and represented digitally using a process called sampling. Data is collected about a sound wave or video frame at set intervals; this data is then used to recreate the sound or video in a digital format.

Compression Techniques

• Lossless compression: This allows the original data to be recovered exactly. It is often used in situations where absolutely no data can be lost, such as text files or scientific data.
• Lossy compression: This does not allow for the exact original data to be recovered. Some information is lost during compression, hence the term 'lossy'. It is often used in images, audio and video where some loss of quality will not be noticed by the human eye or ear.

Error Detection and Correction

• Parity check is a simple error detection technique to ensure that the total number of 1-bits in the string is even or odd.
• Checksum is a count of the number of bits in a transmission unit that is appended to the data and used for error detection.
• Cyclic Redundancy Check (CRC) is a more complex method based on mathematical algorithms. It's used for error checking in networks and storage devices.