Representing Characters

Bit Depth and Capacity: The capacity of a character set is exponentially related to its bit depth. A 7-bit system provides $2^7 = 128$ unique codes, while an 8-bit system provides $2^8 = 256$ codes.

Logical Ordering: Character sets are typically organized sequentially. For example, if 'A' is represented by $65$, 'B' will be $66$, and 'C' will be $67$. This allows for efficient sorting and mathematical comparison of text data.

Control Characters: Not all codes represent visible symbols; the first 32 codes in ASCII are reserved for 'control characters' like 'Line Feed' or 'Escape', which manage hardware behavior.

ASCII (American Standard Code for Information Interchange): Originally a 7-bit standard designed for English text. It includes uppercase and lowercase letters, digits $0-9$, and basic punctuation.

Extended ASCII: An 8-bit evolution that adds 128 additional slots (total 256). These are used for mathematical symbols, graphical characters, and accented letters for Western European languages.

Unicode: A universal standard designed to represent every character from every language, including ancient scripts and modern emojis. It typically uses 16 bits ($65,536$ combinations) or more (e.g., UTF-8, which uses variable lengths).

Storage Calculation: To find the file size of a text string, multiply the number of characters by the bits per character. For example, a 10-character string in 8-bit ASCII requires $80$ bits ($10$ bytes).

The $2^n$ Rule: Always use this formula to determine how many characters can be represented. If an exam asks how many bits are needed for 500 characters, you must find the smallest $n$ where $2^n \ge 500$ (which is $n=9$).

Case Sensitivity: Remember that 'A' and 'a' have different binary codes. In ASCII, uppercase letters always have lower denary values than their lowercase counterparts.

Sequential Logic: If you are given the code for one letter, you can find the code for the next by adding 1. Do not waste time memorizing the whole table; just know the starting points (e.g., 'A' = 65, 'a' = 97).

Units Check: Pay attention to whether the question asks for the answer in bits or bytes. Divide bits by 8 to get bytes.

Confusing Bits and Characters: Students often mistake the number of bits for the number of characters. 8 bits does NOT mean 8 characters; it means 1 character represented by 8 bits, allowing for 256 possible variations.

ASCII and Emojis: A common error is assuming ASCII can store emojis. ASCII is strictly limited to basic text; only Unicode has the capacity for complex symbols and emojis.

Fixed vs. Variable Width: While ASCII is always fixed-width (e.g., 8 bits), some Unicode encodings like UTF-8 are variable-width, meaning different characters can take up different amounts of space.

Data Compression: Understanding character encoding is vital for text compression (like Huffman coding), which reduces file size by using fewer bits for frequently occurring characters.

Network Protocols: When two computers communicate, they must agree on the character set (the 'encoding') in the header of the data packet, or the text will appear as 'mojibake' (garbled symbols).