Nand2Tetris

(Usage hints for this presentation)

IT Systems, Summer Term 2025
Dr. Jens Lechtenbörger (License Information)

Chair of Machine Learning and Data Engineering (Prof. Gieseke)
Dept. of Information Systems
University of Münster, Germany

1. Introduction

Video by co-creator of Nand2Tetris

1.1. Today’s Core Question

How to start with Nand2Tetris?

1.2. Learning Objectives

Build simple chips with HDL
Simulate chips in Hardware Simulator

1.3. Retrieval Practice

What do you remember about Part 1 of IT Systems?
Other parts?

1.4. Recall: Goal of Part 1

Recall: Build general-purpose, programmable computer; here, the Hack platform
- Programmable in machine language
- Built from chips and gates specified in hardware description language (HDL)
  - (Gates are “simple” chips)
- Nand2Tetris with sequence of projects

Agenda

1. Introduction
2. Preview
3. Projects of Nand2Tetris
4. And Gate
5. Nand2Tetris Resources
6. Conclusions

2. Preview

2.1. Hack Machine Language

Hack CPU executes instructions in machine language

The brains of computers reside in processing units, or processors for short. In case of Hack there is a single central processing unit, or CPU. This CPU continuously executes instructions. Each instruction is just a certain bit pattern, which is interpreted by the CPU to determine what operation to perform on what operands.
- Each Hack instruction consists of 16 bits
  - Consider increment of variable: i = i + 1
  - Translated into two Hack instructions
  - 0000000000010000 (A-instruction, starts with 0, binary number for 16)
    - Human-readable assembly language instruction: @16
    - Used here to specify memory (RAM) location for value of variable
  - 1111 110111 001 000 (C-instruction, starts with 1, encodes operation)
    - Human-readable assembly language instruction: M=M+1
    - 6 red bits specify operation (compute M+1), 3 blue bits specify where to store the result (in M, the memory location for our variable)
  Here, you see an example how the increment of some variable might be represented by two instructions in the Hack machine language. Notably, different parts of the instruction’s bit pattern serve different purposes.
  
  You can ignore the details for now.
- Modern processors behave similarly
  - Later: Fetch-Decode-Execute Cycle
    - Fetch next instruction from memory, decode bits to determine operation and operands, execute
    - Von Neumann architecture (von Neumann 1945)
  Similarly to the case of Hack, also modern processors execute architecture-specific machine instructions, which are fetched from RAM, decoded, and then executed.
  
  This computer architecture is known as von Neumann architecture, following a seminal description by John von Neumann in 1945.

2.2. Preview: Hack Computer Architecture

Hack Computer Architecture

“Hack Computer Architecture” under CC0 1.0; from GitLab

This figure shows major elements of the Hack computer architecture, which will be explored in great detail in upcoming weeks.

In Hack, two types of memory are distinguished: Random-Access Memory, or RAM for short, and Read-Only Memory, ROM for short. Random-access means that data can be read and changed in any order, at the same speed irrespective of the location, while read-only means that such memory receives its contents upon fabrication, which can only be read, again in any order, but not be changed. Data items in memory are equal-sized bit strings, e.g., of length 8 bits to form bytes, or words of 16 bits in Hack. Addresses specify which data item to read or write.

Octagons visualize active components, in particular the Arithmetic Logic Unit, ALU for short, which performs computations and is the major part of the computer’s CPU. The ALU executes operations that are specified by instructions which in turn are retrieved from ROM. Depending on the specific instruction, a control logic determines on what operands the ALU operates, including values stored in registers or in RAM, and if and where to store a result.

In addition, registers are small storage devices whose size and number depends on the architecture of the computer. In Hack, the following three registers exist, each of which contains a word of 16 bits:

First, the program counter stores the address of the next instruction to execute. Thus, this register is wired to the ROM’s address input.

Second and third, the registers A and D can store addresses as well as inputs for and results of ALU operations.

Similarly to Hack, modern computers contain processing units, registers, and memory. Differently from Hack, RAM stores not only data but also instructions. Thus, in our computers, we can simply load new programs into RAM to execute them, while in Hack, ROM chips would have to be replaced. In fact, out computers follow the model of the von Neumann architecture mentioned previously.

3. Projects of Nand2Tetris

3.1. What to Expect in a Project

Projects focus on successively more complex chips

Our goal is to build a digital computer in a sequence of projects, which aim to build successively more complex chips.
- From simple logic gates to entire computer
  
  We start from a simple logic gate for the Boolean function Nand, and we end at a programmable computer.
- Digital/binary devices with bit as basic unit of information
  - Bit = Logical state with two values: true/false or 1/0
  - Data and instructions to be represented as sequences of bits
  Boolean logic is a suitable starting point for building computers as we consider electrical devices starting from two basic states, namely electrical current being present or not. These two states can be interpreted a a single bit of information, carrying either a Boolean value true or false, or alternatively an Integer value 1 or 0.
  
  While we first manipulate individual bits based on logical operations, we later see how to encode numbers and machine instructions with sequences of bits, for which you saw a sketch on an earlier slide.
- Chips come with specifications/interfaces (and tests)
  - What to do. Abstraction!
  All the chips will come with specifications and interfaces specifying what each chip is supposed to do. Your task is to come up with an implementation specifying how to perform those operations. Clearly, those specifications provide a level of abstraction over the implementation.
- Results/implementations for each project are building blocks for subsequent ones
  - Abstraction and modularity!
  Then, you will use your implementations in subsequent projects as building blocks for even more complex pieces of the computer. Again, this provides a level of abstraction and also modularity.
  
  Thus, we break down the complex task of building a computer into more manageable modular units.
- You work on projects individually
  - Without immediate impact on grading, but lasting impact on brains (and, thus, on exam results)
  - (Solutions can be found on the web)
  As a side note, you work on those projects individually, and we do not look at your results. Thus, the project work does not have an immediate impact on grading, but it will have a lasting impact on your brain, and therefore also on the grading in the final exam. In case you get stuck, note that you will be able to find solutions out there on the web.

3.2. What to Expect in Project 1

Project 1
1. Given: Nand(x, y), false
  
  x y Nand(x, y)
  
  0 0 1
  
  0 1 1
  
  1 0 1
  
  1 1 0
  - Nand is a binary Boolean function
    - Specified by truth table to right
    - 0 represents false, 1 represents true
  In Project 1, we start from Nand and false. Thus, we suppose that a Nand gate as well as the constant false are given to us. In reality, gates are usually fabricated from different types of transistors, which is beyond class topics. Also, we do not consider quantum computing.
  
  Here you see the notation Nand of x and y, which indicates that Nand can be understood as binary function, i.e., as function that takes two arguments. As those arguments are interpreted as Boolean values, Nand is a binary Boolean function.
  
  Boolean functions can be specified by truth tables, such as the one shown here. Truth tables specify what output value is computed by the function for each of the possible input value combinations.
  
  The truth table for Nand contains four rows because Nand is a function with two arguments, each of which can have either of two values, for a total of four combinations. We see that Nand of x and y results in 1 (or True) unless both arguments have the value 1 (or True).
1. Learn about Boolean logic
  
  Later on, you will learn about Boolean logic and build successively more complex logic gates and chips, starting from Nand. Some possible steps are outlined next.
2. Implement sequence of chips (from specifications)
  1. Not(x)
    - Not flips its argument: true = Not(false), false = Not(true)
    - Implementation: Not(x) = Nand(x, x)
    First, using just Nand, we can build a chip for the function Not, which takes a single Boolean value as input argument and flips it, i.e., Not turns 1 into 0 and vice versa.
    
    Please take a moment to convince yourself that Not of x equals Nand of x with itself.
    
    Besides, Not can compute true from false, which is why we can say that we start our journey towards a computer only from Nand and false.
  1. And
    - True if and only if all arguments are true; revisited subsequently
    Having a chip for Not in addition to Nand, it makes sense to build a chip for the And function, which only produces 1 as output if all input arguments are equal to 1.
  2. Xor, Or, Mux, and several more…

x	y	Nand(x, y)
0	0	1
0	1	1
1	0	1
1	1	0

4. `And` Gate

4.1. Specification of `And` Gate

Three files for binary function And(a, b)

Chips in Nand2Tetris typically come with three files as follows.
1. HDL file with interface and specification, And.hdl
```
// This file is part of www.nand2tetris.org
// and the book "The Elements of Computing Systems"
// by Nisan and Schocken, MIT Press.
// File name: projects/01/And.hdl

/**
 * And gate:
 * out = 1 if (a == 1 and b == 1)
 *       0 otherwise
 */

CHIP And {
    IN a, b;
    OUT out;

    PARTS:
    // Put your code here:
}
```
Most importantly, an HDL file describes the interface of a chip in terms of input and output pins, here starting at line 12. In addition, a comment in lines 6 to 10 specifies the expected behavior. Here, the output should be 1 exactly if both inputs are 1.
1. File And.cmp
  
  a b out
  
  0 0 0
  
  0 1 0
  
  1 0 0
  
  1 1 1
  - Test cases (here, truth table)
  Second, test cases specify what the chip under construction should compute for given inputs.
2. File And.tst
  - Test file for hardware simulator
  - To check implementation against test cases
  Finally, a test script can compare expected results against actually computed values.

a	b	out
0	0	0
0	1	0
1	0	0
1	1	1

4.2. Implementation of `And` Gate (1/3)

What an And gate should do
- Specification: out == 1 if and only if a == b == 1
  Figure under CC0 1.0
- Interface in HDL skeleton: And.hdl

CHIP And {
    IN a, b;
    OUT out;

    PARTS:
        // Put your code here:

}

4.3. Implementation of `And` Gate (2/3)

Idea to implement And gate
- Gate logic: And(a, b) = Not(Nand(a, b))
  Figure under CC0 1.0
- Interface in HDL skeleton: And.hdl

CHIP And {
    IN a, b;
    OUT out;

    PARTS:
        // Put your code here:

}

4.4. Implementation of `And` Gate (3/3)

Implementation of And gate
- Gate logic: And(a, b) = Not(Nand(a, b))
  Figure under CC0 1.0
- Completed HDL file: And.hdl

CHIP And {
    IN a, b;
    OUT out;

    PARTS:
        Nand(a = a, b = b, out = aNandB);
        Not(in = aNandB, out = out);
}

5. Nand2Tetris Resources

5.1. Nand To Tetris Software

Download Java software: https://www.nand2tetris.org/software
- (Java runtime needed. Install first.)
- ZIP archive, contains tools and project files
  - I had to do this in the tools subdirectory: chmod u+x *.sh
- We start with the Hardware Simulator
- (Later on, we also use the CPU Emulator)
Nowadays, the Nand2Tetris team recommends an online IDE: https://nand2tetris.github.io/web-ide/chip/
- Try above Java variant as exercise in digital sovereignty

5.2. Hardware Simulator

Previous And implementation in Hardware Simulator
“Screenshot of Hardware Simulator for Nand to Tetris” under GPLv2; from GitLab
- Major window parts
  - HDL file in lower left, test script on right
  - Values of “Input pins” can be entered, resulting “Output pins” and “Internal pins” can be computed
  - Note message area at bottom. If not shown, resize window!

5.3. Textbook for Nand to Tetris

(Nisan and Schocken 2005) The Elements of Computing Systems
- Book chapters are available online: https://www.nand2tetris.org/course
  - Hyperlinked from “reading person icons”
  - We use Chapters/Projects 1, 2, 4, 5
Download chapters now, start to read and work on Project 1
- Note “Tips” and “Steps” at end of Chapter 1

6. Conclusions

6.1. A Related Story, 2021

From Nand to Zero-Day Exploit
- Google Project Zero on attack software targeting iPhones
  - Discussion with hyperlink to https://www.nand2tetris.org/!
  - Summary
    - NSO Group used logic operations (And, Or, Xor, Xnor; functionally complete) of an image format (JBIG2, mostly outdated) to hijack iPhones
    - 70,000 segment commands to define computer architecture with registers and 64-bit adder
  - Quote
    - “The bootstrapping operations for the sandbox escape exploit are written to run on this logic circuit and the whole thing runs in this weird, emulated environment created out of a single decompression pass through a JBIG2 stream. It’s pretty incredible, and at the same time, pretty terrifying.”
- Quotes regarding working at Project Zero
  - “learn about coding and how computers work”
  - “learning the fundamentals of programming, operating systems, and machine architecture is a great starting point”

6.2. Summary

Nand2Tetris guides you to build a computer
- Based on abstraction and modularity
- Weekly projects, with guidance from us

6.3. Q&A

Uncovering questions

“Uncovering questions” under CC0 1.0; background changed from Pixabay

Bibliography

Neumann, John von. 1945. “First Draft of a Report on the EDVAC.” University of Pennsylvania. https://web.mit.edu/STS.035/www/PDFs/edvac.pdf.

Nisan, Noam, and Shimon Schocken. 2005. The Elements of Computing Systems: Building a Modern Computer from First Principles. The MIT Press. https://www.nand2tetris.org/.

License Information

Source files are available on GitLab (check out embedded submodules) under free licenses. Icons of custom controls are by @fontawesome, released under CC BY 4.0.