The process of building a modern computer system involves the integration of both hardware and software components, starting from the basic building blocks of digital logic to the development of a sophisticated software stack. There is a structured approach which will help learners to construct a computer system incrementally ensuring a deep understanding of each layer's functionality and interaction.

CONSTRUCTION OF HARDWARE

Logic Gates and Boolean Algebra: The foundation of a computer's hardware is built on the construction of basic logic gates (AND, OR, NOT) using Nand gates and Boolean algebra principles.
ALU(Arithmetic Logic Unit): Developing the ALU, which performs essential arithmetic and logical operations, forming the core computational component of the CPU.
Central Processing Unit (CPU): Designing the CPU to execute a set of instructions, manage data flow, and interface with memory and I/O devices. This includes the development of control logic and the instruction set architecture (ISA).
Memory Architecture: Creating both RAM and ROM structures to handle data storage and retrieval efficiently, and implementing memory addressing schemes.
Input/Output (I/O) Devices: Designing interfaces for peripheral devices such as keyboards, displays, and secondary storage units.
Clock and Control Logic: Implementing clock generation and control logic to synchronize and manage the operations of various hardware components.

DEVELOPMENT OF SOFTWARE

Machine Language: Defining a low-level machine language that the CPU can interpret and execute directly.
Assembler: Building an assembler to translate human-readable assembly language into machine code, facilitating easier programming of the CPU.
Virtual Machine (VM): Developing a virtual machine that provides an abstraction layer, allowing the execution of high-level language code on the hardware.
High-Level Language (HLL): Designing a high-level programming language (e.g., Jack) and creating a compiler to convert high-level language code into virtual machine instructions.
Operating System (OS): Constructing an operating system to manage hardware resources, provide a file system, support multitasking, and offer a user interface.
Application Development: Developing applications, such as text editors, games, and web browsers, to demonstrate the capabilities of the computer system and provide practical usage scenarios.

After hardware construction and software development, the next phase is integrating and testing. You have to make use of simulation and emulation tools like VirtualBox and Logisim to debug and test the hardware component and the entire system virtually before physically implementing them. You might have to test each software and hardware unit individually to ensure functionality and reliability. After construction of the system, you have to conduct a comprehensive systems test to validate the integrated hardware and software ensuring all components operate together seamlessly.

For a deeper dive into this fascinating process, explore Nand to Tetris course. This project-centered learning experience allows you to construct a 16-bit computer yourself, from the fundamental logic gates up, providing a hands-on understanding of how modern computer systems are built layer by layer.