all hardware and software components are built completely from scratch to fully learn and understand how computers work. The ultimate goal is to create a fully functional 16-bit computer capable of running Tetris.

The foundation of any computer system is built on logic gates and boolean logic. In this phase, we construct a large collection of 1-bit and 16-bit logic gates from scratch.

• Basic Gates: AND, OR, NOT, NAND, NOR, XOR, XNOR
• Composite Gates: Multiplexers, Demultiplexers, Adders, Subtractors
• 16-bit Versions: Expanding 1-bit logic gates to operate on 16-bit data

Building on the logic gates, we develop the Arithmetic Logic Unit (ALU), which is responsible for performing arithmetic and logic operations.

• Mathematical Operations: Addition, Subtraction, Bitwise operations
• Logical Operations: AND, OR, NOT, NAND, NOR, XOR, XNOR
• 16-bit ALU: Capable of executing complex operations on 16-bit data

Memory is crucial for storing data and instructions. This phase focuses on creating various sizes of RAM chips and clocked chips, including D flip-flops.

• Basic Memory Elements: D Flip-Flops, Latches
• RAM Chips: 4-bit, 8-bit, 16-bit, and beyond
• Clocking Mechanisms: Ensuring synchronized data storage and retrieval

With the hardware foundation in place, we define and test programs written in the Hack flavor of Assembly language.

• Instruction Set Architecture (ISA): Definition of the Hack assembly language
• Test Programs: Simple programs to test and validate the hardware components

The Central Processing Unit (CPU) integrates all hardware components into a single chip capable of executing instructions.

• Control Unit: Manages the execution of instructions
• Data Path: Routes data between the ALU, memory, and registers
• Integration: Combining all components to form a cohesive CPU

The assembler translates Hack machine language into binary code that the CPU can execute.

• Syntax Parsing: Converts assembly language into machine code
• Code Generation: Outputs binary files ready for execution

The first part of the Virtual Machine (VM) translation as part of a two-step compilation process handles basic VM bytecode and translates it into machine code.

• Stack Arithmetic: Handling basic stack operations
• Memory Access: Translating memory access commands
• Code Translation: Converting VM code to Hack assembly

In this phase, we extend the capabilities of the VM translator to handle more complex commands, including program flow and function calling.

• Program Flow: Translating conditional and unconditional branching commands
• Function Calling: Handling function calls and returns
• Advanced Memory Access: Managing memory segments like pointers, static, and temp

The high-level language Jack is introduced, providing a more abstract and user-friendly way to write programs.

• Space Invaders: A basic version of Space Invaders, implementing the core mechanics
• Syntax and Semantics: Definition of the Jack language, including syntax and semantic rules
• Standard Library: Basic standard library functions for string manipulation, I/O, and mathematics
• Sample Programs: Example Jack programs demonstrating language features

The first part of the Jack compiler translates Jack high-level language into VM code.

• Syntax Analysis: Parsing Jack code into an deriveration tree (recursive descent parsing)
• Code Generation: Translating the AST into VM code
• Error Handling: Detecting and reporting syntax and semantic errors

The second part of the Jack compiler focuses on optimizing and finalizing the translation process from Jack to VM code.

• Optimization: Improving the efficiency of the generated VM code
• Advanced Code Generation: Handling complex language constructs and features
• Comprehensive Testing: Extensive testing to ensure correctness and performance

With the hardware and software infrastructure in place, we develop a simple operating system to manage the computer's resources and provide essential services.

• Memory Management: Handling memory allocation and deallocation
• Process Management: Managing program execution and multitasking
• I/O Handling: Providing input and output functionalities