9/10: ISA basics, bit width, color depth, and MATLAB fundamentals

Instruction Format and ISA Basics

• Instruction format runs through an ISA: fixed-length vs variable-length instructions. Example: a 16-bit instruction on a 16-bit system is a single unit of code to be loaded into the CPU and executed. $ext{Instruction length} = 16 ext{ bits}$
• Addressing mode flag: a single bit can indicate how an address should be interpreted (direct vs indirect addressing).
• Address space: memory is byte-addressable; each byte has an index (0, 1, 2, …).
• Operations combine an opcode with addresses or immediates; sometimes an operation like ADD uses two operands (addresses or immediates).
• Simpler designs favor fixed-length instructions for predictability; more complex designs can use variable-length instructions but are harder to implement efficiently.
• IC design goal: balance between simplicity (RISC) and expressiveness/power (CISC). CISC can have long, powerful instructions but higher energy; RISC emphasizes energy efficiency and simpler decoding.
• Modern chips: manufacturing nodes (e.g., 3 nm) enable more cores and efficiency; bit width (e.g., 64-bit) is common for modern CPUs.
• Color depth and display impact: true color commonly uses 24 bits (8 bits per channel for RGB).
• Color math: with 8 bits per channel, per-channel max is $2^{8}-1 = 255$; total color combinations for RGB is $256^3 = 2^{24} = 16{,}777{,}216$.
• Backward compatibility: newer software/hardware often supports older instruction sets or software through compatibility modes; a 64-bit system can often run 32-bit software, sometimes by padding or emulation. For example, older 32-bit programs can run on a 64-bit OS, with higher bits set to zero where needed. If software is 64-bit, a 32-bit program may still be supported via compatibility layers.
• MATLAB and software alignment: MATLAB on modern machines typically runs as a 64-bit application; 32-bit versions exist but are increasingly uncommon.
• Example bit/byte scales: 16-bit, 32-bit, 64-bit representations are common; max unsigned values include $2^{16}-1 = 65535$ and, for 8-bit color channel, $2^{8}-1 = 255$.
• Data width and performance trade-offs influence system design (e.g., fixed-length ISA simplifies CPU design and energy management; longer, variable-length instructions can be more powerful but cost more energy).

MATLAB Basics: Workspace, Scripts, and Command Window

• MATLAB workspace shows all current variables; you can inspect with a command like WHO or WHOS.
• Files: MATLAB scripts use the extension $ext{.m}$.
• Command window: quick line-by-line execution; assignments are simple, e.g., $a = 1 + 2;$ creates a and stores the value 3.
• MATLAB is case sensitive for variable names.
• Variables do not require explicit type declarations; MATLAB uses dynamic typing (type checking is not forced at compile time).
• Common data types: double (default numeric type, 64-bit real), 64-bit storage; for a numeric array, storage is shown by WHOS; 64-bit means eight bytes per element.
• Basic commands:
  • Create variable: $a = 10;$
  • Check workspace: $who;$ or $whos;$
  • Suppress output with a semicolon: $b = [1,2,3];$
• MATLAB documentation and community help are widely used; MATLAB Central and forums provide examples and shared code.
• Important concepts:
  • Variables are named with first letter, then letters, digits, or underscores; names are case sensitive.
  • A line of code is called a statement or instruction and can end with a semicolon to suppress output.
  • A line of code is text; a program is a collection of such lines (scripts).
  • For numeric formatting, MATLAB uses formatting verbs similar to C printf via fprintf.

Data Types, Output, and Formatting in MATLAB

• Format specifiers in MATLAB-like fprintf:
  • $\%d$ for integer
  • $\%f$ for floating point
  • $\%c$ for a single character
  • $\%s$ for a string
  • You can also specify width and precision, e.g., $$, which controls minimum width and decimal places.
• Example: printing an integer and a float in one statement:
  • $fprintf('A =$
• Flags and formatting options:
  • '-' left-justify within the field
  • '+' always show sign
  • ' ' leading space for positive numbers
  • '0' pad with leading zeros
  • Width controls total field width; precision controls number of decimals
• Printing multiple values without hard-coding each line:
  • Use a for loop: for i = 1:10, fprintf('i = %d\n', i); end
  • This avoids repeating code (vs hard-coding ten lines).
• Printing matrices or strings can be controlled to show subsets or sub-strings as needed.
• Numeric prefixes and base representations (e.g., decimal, hex) can be used with appropriate formatting, though d, f, c, s are the core ones for common use.

Control Flow and Practical Tips

• Loops (for, while) are essential for repetitive tasks; use them to avoid hard coding.
• Use semicolons to suppress intermediate outputs in scripts to keep the workspace clean.
• Be mindful of type behavior when mixing integers and real numbers; MATLAB implicitly casts numbers as needed but no strict type checking like some other languages.
• Understanding bit width and data representation helps reasoning about performance, memory, and compatibility across platforms.

Quick Recall Cards

• 24-bit color depth means 8 bits per channel; max per channel is 255; total colors = $256^3 = 2^{24} = 16{,}777{,}216$.
• A 16-bit instruction is $16 ext{ bits}$; higher bit widths enable larger address spaces and more complex instructions.
• In fixed-length ISA, every instruction has the same length; simplifies decoding and energy usage.
• In MATLAB: variables are created by assignment; no explicit type declaration; use WHOS to inspect variables.
• printf/fprintf formatting basics: %d, %f, %c, %s; width/precision control via e.g. %4.1f; use -/+ and 0 padding as needed.