Problem Sets 1

ABSTRACT

This problem set serves as the introduction to Low-Level Data Representation. It covers the fundamental mechanics of bit manipulation, integer signedness, and the serialization of characters into the UTF-8 encoding standard.

Problem Categories

Bitwise Fundamentals

• Bitwise Is Even: Determining parity using bitwise AND instead of arithmetic modulo.
• Count 1 Bits: Implementing population count logic to tally set bits in a word.
• Check if Bits Start with ‘10’: Pattern matching for specific bit sequences, essential for protocol headers.
• Extract Least Significant 16 Bits: Isolating the lower half of a 32-bit integer.
• Extract Most Significant 16 Bits: Isolating the upper half of a 32-bit integer.
• Extract Lowest N Bits: A generalized approach to creating bitmasks for variable-width data extraction.

Integer Representations

• Binary String to Signed 8-bit Integer: Interpreting small-scale Two’s Complement values.
• Convert Binary String to Signed 32-bit Integer: Handling standard integer signed-ness in C.
• Convert Binary String to Unsigned 32-bit Integer: Converting raw binary strings to positive integer magnitudes.
• Printing Char and Integer Representations: Exploring how the same 8-bit pattern is interpreted as a character vs. a numeric value.
• Printing Char and Integer Representations Backwards: Advanced iteration and bit-field inspection.

Character Encodings (ASCII & UTF-8)

• Is ASCII: Validating the 7-bit standard within an 8-bit byte.
• Capitalize ASCII: Using bit-toggling to transform character case without branching.
• To Lowercase: Applying bitwise offsets to normalize character casing.
• UTF-8 Codepoint Size: Analyzing leading bytes to determine the length of a multi-byte character.
• Encode UTF-8: Mapping a Unicode codepoint into its variable-width byte sequence.
• Count UTF-8 String Length: Distinguishing between byte count and logical character count.
• Find UTF-8 Codepoint at Index: Navigating a variable-width stream to locate a specific character.
• Extract a UTF-8 Substring by Codepoint Indices: Implementing logical slicing on encoded data.
• Check if a Codepoint is an Animal Emoji: Validating specific hexadecimal ranges within the Unicode space.

Technical Summary

Related Toolkits

• C Syntax: Essential for using bitwise operators (&, |, ~, ^, <<, >>).
• Counting: Used to determine the number of possible values in different bit-widths (e.g., $2^{16}$ vs $2^{32}$).
• Lecture: Strings and Data: Theoretical background on how these encodings were designed.