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| author | Frederick Yin <fkfd@fkfd.me> | 2022-08-18 20:44:33 +0800 |
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| committer | Frederick Yin <fkfd@fkfd.me> | 2022-08-18 20:44:33 +0800 |
| commit | 9b4dc7b918935c31659e72cf36c1af0ea4fa8981 (patch) | |
| tree | 5f6ec12923ebd7770e077618936e8d6e38553228 /docs | |
| parent | 18cb29e1a166eddcc783838f3171c9f000d45577 (diff) | |
New post: projects/nand2tetris_1
Diffstat (limited to 'docs')
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But the few that do, are here. Projects below are sorted reverse chronologically (most recent first). +## [nand2tetris, Part 1](nand2tetris_1) + + + +In July 2022 I enrolled in a course called nand2tetris. In part one of +this course I built a computer from NAND gates and ran assembly on it. It +was great fun. + ## [SIRTET](sirtet)  diff --git a/docs/projects/nand2tetris_1.md b/docs/projects/nand2tetris_1.md new file mode 100644 index 0000000..12a8704 --- /dev/null +++ b/docs/projects/nand2tetris_1.md @@ -0,0 +1,947 @@ +# nand2tetris, Part 1 + +2022-08-18 + +> _"It takes building one yourself to realize you don't deserve a computer."_ + +On 2022-07-22, I finally clicked into the bookmark that had been sitting +in my "University readlist" folder, untouched, since last August. Somehow +I justed wanted to build a computer all of a sudden. + +First a bit of background. [Nand to Tetris](https://www.nand2tetris.org/) +is a course available online by Noam Nisan and Shimon Shocken that teaches +you how to build a modern (albeit extremely simple) computer all the way +up from NAND gates. The course is divided in two parts, to which I have +given the following nicknames: + +- Part 1, NAND to Computer +- Part 2, Computer to Tetris + +The first part of the course consists of 6 projects. On 2022-08-16 +I completed all of them. In this blogpost I will recap what I learned from +the course, and from my mistakes. __WARNING: There will be spoilers. If +all you need is reasons why you should enroll, go to [Course +review](#course-review)__. + +I've uploaded my current projects to [this git repo](https://git.fkfd.me/nand2tetris.git/). + +## Project 01: Elementary gates + +In this project I built a few basic logic gates, such as AND, XOR, and the +(De)Mux, using a custom HDL language invented for the course. Here is the +code for the AND gate: + +``` +CHIP And { + IN a, b; + OUT out; + + PARTS: + Nand(a=a, b=b, out=nout); + Not(in=nout, out=out); +} +``` + +Graphically, the HDL describes the following schematic: + + + +Here `a`, `b` and `out` are hardcoded, but `nout` is an arbitrary name +I gave to the internal pin. If we further substitute the implementation of +`Not` in `Nand`, this is what _actually_ lives on the silicon: + + + +Once we have written this HDL code, we can encapsulate the AND gate in the +following symbol, which is in essence two NAND gates in a trenchcoat: + + + +And this is one of the few chips that have so few pins exposed (hence +"elementary") that you can craft a truth table for it, and thus can test +them manually. + +<details> +<summary> + <b>How I built and optimized the XOR gate by toying with boolean + expressions (click to expand)</b> +</summary> + +Here is the truth table of XOR, and you have to implement it with chips +you already made, which are AND, OR, NOT, and NAND. + +``` + a | b | out +---|---|---- + 0 | 0 | 0 + 0 | 1 | 1 + 1 | 0 | 1 + 1 | 1 | 0 +``` + +The solution is not immediately obvious (you can skip this part if you +find it so). It is proven that, given any truth table of finite columns, +you can construct a boolean expression satisfying it using what's called +a "disjunctive normal form". Here's how it works. First you extract every +row that outputs 1: + +``` + a | b | out +---|---|---- + 0 | 1 | 1 + 1 | 0 | 1 +``` + +Then we tie a NOT to each 0 input (excuse the pun), thus synthesizing two +sufficient conditions so that <code>out=1</code>: + +``` +(NOT a) AND b => out=1 +a AND (NOT b) => out=1 +``` + +Finally, we OR them both, resulting in a single boolean expression: + +``` +((NOT a) AND b) OR (a AND (NOT b)) +``` + +From a pragmatic perspective, our job is done. But the whole premise of +nand2tetris is that, we're building every chip out of NAND gates, and I'm +challenging myself to use as few as possible. So let's count how many NAND +gates we need to make a XOR. + +``` +Gate | # of NAND gates +-----|---------------- +NAND | 1 +NOT | 1 +AND | 2 +OR | 3 +XOR | ? +``` + +``` +((NOT a) AND b) OR (a AND (NOT b)) + ^ ^ ^ ^ ^ + 1 2 3 2 1 +``` + +That's 9 in total. Can we optimize it? Let's try eliminating the OR first, +based on the fact that <code>a OR b = NOT((NOT a) AND (NOT b))</code>: + +``` + ((NOT a) AND b) OR (a AND (NOT b)) += NOT((NOT((NOT a) AND b)) AND (NOT(a AND (NOTb)))) +``` + +At first glance this might seem more complicated, but remember, +<code>NOT(a AND b) = a NAND b</code>… which is exactly our atomic building +block! We continue our equation: + +``` += ((NOT a) NAND b) NAND (a NAND (NOT b)) +``` + +Since NOT and NAND are both made of one single gate, our optimized number +of gates is 5. (However, this optimization did not matter for a reason +I will explain later.) +</details> + +There were many other chips I was already familiar with, so I implemented +them with little trouble apart from the HDL syntax. + +## Project 02: ALU + +The goal of building a computer in this theoretical approach is to conjure +up a way to make a pool of NAND gates capable of thinking. This project +does exactly that. Yes, you are right: I built an ALU. + +The fundamental idea of an ALU is that, you give it two inputs `x` and `y` +and pick a function `h`, and for some reason it outputs `h(x, y)` where +`h` is one of the following: + +``` +0, 1, -1, // constant value +x+y, x-y, y-x // arithmetics +x, y, -x, -y, !x, !y, // single variable function +x+1, y+1, x-1, y-1, // one variable + constant +x&y, x|y // boolean operation +``` + +You supply 6 bits known as "control bits" that let the ALU decide what +function you want. They are: + +- `zx`, `zy`: coerce x or y to zero when set +- `nx`, `ny`: negate x or y when set (binary NOT) +- `f`: performs binary arithmetics when set, boolean operation otherwise +- `no`: negate output-to-be + +But how do you know when you need to negate or zero the operands? Doesn't +this call for an `if` statement? Well, in project 01 I made a chip named +`Mux16` and it is _tremendously_ helpful. It's the hardware embodiment of +`if () ... else ...`. + + + +(In reality we are using the 16-bit version, but in principle they're the +same.) + +This means I just need to hook `nx` and `zx` to `sel` pins, and route +`a`'s and `b`'s somewhere. + +The HDL that does this job for `x` is: + +``` +Mux16(a=x, b=false, sel=zx, out=zdx); // false = all 0's +Not16(in=zdx, out=ndx); +Mux16(a=zdx, b=ndx, sel=nx, out=px); +``` + +Graphically: + + + +(The order of the muxes matters, because when `zx = nx = 1`, this logic +configuration yields `~0 = -1` while the other way gives you 0.) + +The same goes for `y`. Now that we have the processed version of `x` and +`y`, denoted `px` and `py`, it's time to force this pile of imaginary NAND +gates to do math for us. The boolean AND operation is trivial, so we will +only be talking about the Adder, which is a chip that takes two binary +numbers `x` and `y` and outputs `(x+y) % 65536`, that is, carries every +bit except the MSB. + +But wait! Didn't we just see "x-y" and "y-x"? How can an Adder possibly do +that? Note that there is no "Subtractor"; to do `x-y` you simply calculate +`~(~x + y)` where `~` denotes bitwise negation, thanks to 2's complement. + +<details> +<summary><b>Proof that <code>x-y = ~(~x + y)</code></b></summary> + +We know in 2's complement, + +``` +~x + x = 0xffff = -1 <==> ~x = -1 - x +``` + +Add y to both sides, we get + +``` +~x + y = -1 - x + y +``` + +Therefore, by means of negation, + +``` +~(~x + y) = -1 - (~x + y) + = -1 - (-1 - x + y) + = -1 + 1 + x - y + = x - y ⌷ +``` +</details> + +(Nisan and Shocken have supplied this course with a table where you can +look up the ALU output given six control bits, or vice versa, but it won't +be a necessity until project 06.) + +In addition to a 16-bit output bus (we call a group of indexable pins +a "bus"), the ALU outputs two flags: `ng` and `zr`. If the final output is +negative, `ng` is set; if it is zero, `zr` is set. The clever thing is, +`ng` is just the highest bit of the output, i.e. `out[15]`, and `zr` is +set iff every bit in `out` is zero. + +That's it, we have completed the ALU! I know y'all are anticipating the +schematics; how can I let you down? + + + +For some reason nand2tetris only provided me with `Or8Way`, which OR's +together 8 bits, so I had to use two of them to do all 16. I tried writing +an `Or16Way` "helper chip" in the project 01 folder, but when I tried to +include it in the ALU, it did not work. Why? + +When you tell the hardware simulator to load a chip, it first looks for +`<chip_name>.hdl` under the working directory; if there's no such file, it +proceeds to look for builtin chips implemented in Java. No other directory +is in its path, even project 01. This explains why the optimization I made +in project 01 does not matter. + +<details> +<summary><b>If it did matter, how many NANDs are there in this ALU?</b></summary> + +It's Python scripting time! I just need to recursively find out how many +NANDs in each subchip, then add them up. The syntax of HDL is pretty +simple, and the script goes as follows (simplified): + +``` +HDL_PROJECTS = ["01", "02", "03/a", "03/b", "05"] + +CHIPS = { + "Nand": 1, + "DFF": 6, # https://commons.wikimedia.org/wiki/File:Edge_triggered_D_flip_flop.svg +} + + +def count_nands(project_path, chip): + # figure out where the HDL is + f = None + for dir in HDL_PROJECTS: + try: + f = open(project_path + dir + f"/{chip}.hdl") + break + except FileNotFoundError: + continue + + if f is None: + print(f"Chip not found: {chip}", file=stderr) + return 0 + + while f.readline().strip() != "PARTS:": + continue + + nands = 0 + line = f.readline() # e.g. " Not (in=in, out=out); // comment" + while line: + code = line.split("//")[0].strip() # e.g. "Not (in=in, out=out);" + if "(" not in code: + line = f.readline() + continue + subchip = code.split("(")[0].strip() # e.g. "Not" + if subchip not in CHIPS: + CHIPS[subchip] = count_nands(project_path, subchip) + print(f"{subchip}\t{CHIPS[subchip]}") + + nands += CHIPS[subchip] + line = f.readline() + + f.close() + return nands + +chip = "ALU" +nands = count_nands("/path/to/nand2tetris/projects/", chip) +print(f"There are {nands} NAND gates in {chip}") +``` + +The output is (vertically aligned): + +``` +Not 1 +And 2 +Or 3 +Mux 8 +Mux16 128 +Not16 16 +And16 32 +Xor 5 +HalfAdder 7 +FullAdder 17 +Add16 262 +Or8Way 21 +There are 1156 NAND gates in ALU +``` + +Pretty sure my algorithm's right. Honestly it's fewer gates than +I imagined because the ALU seemed to do so many things. +</details> + +Most of the chips I made in project 02 are too complex to test by hand, +but fortunately nand2tetris provides test scripts and compare files you +can run in a hardware simulator that simulates the logic described by the +HDL. + +While I was drawing the schematics, a question came to mind: If I set `f` +to zero, will the Adder be working the same way as if `f=1`? + +<details> +<summary><b>Answer</b></summary> + +Yes, it will. Simply put, chips "downstream" do not directly affect those +"upstream" as far as this course is concerned. The implication is that, +when you give an x and a y to the ALU, it does both computations at once: +boolean AND and binary addition. It is the Mux's job to select which +branch to pass downstream, and which one to discard. This is, in +a stretch, called +<a href="https://en.wikipedia.org/wiki/Speculative_execution"> speculative execution</a>. + +<img alt="Schematic of ALU. The AND, Adder, and "f" mux are +highlighted" src="../img/nand2tetris/alu_highlighted.png" /> + +As you see in the highlighted area, <i>both</i> of these gates are +switching internally, and both of them consume power, even when one of +them does not generate useful output. Recall the <code>if</code> statement +in programming: + +``` +if (boolean) { + do_a(); +} else { + do_b(); +} +``` + +Either but not both of <code>do_a</code> or <code>do_b</code> will be run. +This is one of the major mindblowers I came into, and I think it's worth +writing about it. +</details> + +## Project 03: Memory + +In project 02 we made an ALU think, but only once. This is because it +doesn't remember anything. So if we want to build a computer, we need to +make something that keep a record of what has been done, and what is left +to do. + +The D flip-flop (DFF) is a chip that remembers one bit of information for +one clock cycle. It's the fundamental building block for sequential logic +in nand2tetris. Limitations in the simulator forbid building it from NAND +gates yourself, because to do that you would need to wire an output into +the input, which forms an infinite loop which the simulator is incapable +of resolving. Instead, it provides a builtin chip, `DFF`, using which you +can build registers from 1 bit to 16K words. + +Here's how a register works from the user's point of view: + + + +If you give it some data via `in` and pull `load` to logic one, the data +will show up in `out` at the next clock cycle. However as long as `load` +remains zero, `out` does not change, as if "remembering" the data. + +But doesn't the D flip-flop only keep its data for one clock cycle? Yes, +but we can find our way around it. We simply use a Mux as a "valve": it +only lets `in` pass through when `load` is high. Otherwise, we feed `out` +into the DFF again, creating an eternal feedback loop, but this time the +simulator handles it with no problem, because the loop is delayed by one +clock cycle each step. + + + +The RAM I proceeded to build is just an array of arrays of arrays of … of +arrays of registers. Just copy and paste; no thinking required. + +The Program Counter (PC for short) however, ground my brains like jelly in +a blender. Its job is to remember a number, increment it by one each clock +cycle, and set it to some other value when required. The user controls it +using three control pins: `load`, `inc`, and `reset`. The increment +happens when `inc=1`, unless `load=1`, in which case the PC swallows the +data on the `in` bus and spits it out at the next clock cycle, then +increment that value from now on. `reset`, of course, forces the output to +zero. + +It's not hard to think of using the Register for storage and Inc16 (16-bit +incrementer) to do the math. The rest is Muxes, just like this: + + + +There is a problem with this solution. Do you see it? Let's read the chip +specs again carefully: + +``` +if (reset[t] == 1) out[t+1] = 0 +else if (load[t] == 1) out[t+1] = in[t] +else if (inc[t] == 1) out[t+1] = out[t] + 1 (integer addition) +else out[t+1] = out[t] +``` + +Note that the first line tells us that `out` should be zero if `reset` at +the _previous_ clock cycle is one, whereas in the schematic above, `out` +becomes zero as soon as `reset` rises to one, because the Mux is +a combinatorial chip — it does not wait for the clock. So what can we do? +We just need a way to delay `out` by one clock cycle. The only sequential +chip here is the Register, so let's try hooking `out` onto its output +instead: + + + +Simulation tells me that this works perfectly, but deep inside I feel I'm +still extremely sloppy at clocked logic. + +## Project 04: Assembly + +There's no HDL in project 04. Instead, I learned to write assembly. Nisan +and Shocken, once again, invented an assembly language for this very +architecture called HACK. The language understands two sorts of +instructions. But first, we need to imagine we have a computer. + + + +Here you see three devices inside the blue rectangle: ROM, CPU, and RAM. + +- ROM: Read-Only Memory. Our computer fetches and executes instructions + from it. We did not write HDL for it because it's just a read-only + version of the RAM, and it's builtin. +- CPU: An encapsulation of the ALU that works by black magic until project + 05. +- RAM: Random Access Memory. Our computer can read and write data in it. + +HACK assembly provides an extremely rudimentary way to control the CPU. +The key to understanding HACK assembly is the three registers: D, A, and +M. D stands for "Data" (probably). It holds a 16-bit value; so do the +other two. You can do two things to it in our assembly language: + +- Read it as an ALU input +- Write ALU result into it + +A stands for "Address". It works pretty much the same way D does, with +one more added function: + +- Set it to an assemble-time constant + +which can be realized using this line of assembly (or instruction): + +``` +@42 +``` + +<details> +<summary><b>Expand to learn more about the difference between A and D</b></summary> + +In HACK assembly, the A register is the only one you can directly assign +an value to, like we just did. In contrast, if you want to write 42 into +D, you will need to go through two steps: + +``` +@42 // this sets A to 42 +D=A // this copies the value of A, 42, into D +``` + +However, if you need to set A to some non-constant, you have to use +another trick: + +``` +A=D // this sets A to current value of D +``` +</details> + +M stands for "Memory". Note that it is not a register in the literal +sense; it is actually an alias for RAM[A]. For example, + +``` +@42 +M=-1 +``` + +sets the 42nd word (if you count from zero) in RAM to -1, i.e. set all +bits to one. + +We call an instruction an "A-instruction" if it begins with "@" and +"C-instruction" otherwise. By executing a C-instruction the ALU always +computes something — even zero. You can prefix it with a __destination__ +to decide where the result should be saved. You can either pick or not +pick any of the three registers, A, D, and M, resulting in +8 possibilities, like this: + +``` +D+M; // compute D+M, but do not save it anywhere +AD=1; // set A and D to 1 simultaneously +AMD=1 // set A, M and D to 1 simultaneously +``` + +C-instructions can also do something really cool, which is <b>jumping</b>. +The syntax is different from what you might find in an industrial assembly +language. + +``` +@42 +D;JEQ // this jumps to ROM[42] if D=0 +``` + +The <code>JEQ</code> here is a <b>jump instruction</b>. A jump instruction +compares ALU output to zero, and jumps if it is greater/equal/not +equal/etc. + +<details> +<summary><b>What if I want to jump to 42 if RAM[69] is zero?</b></summary> + +Can I just: + +``` +@69 +@42 +M;JEQ // does this work? +``` + +No. <code>@42</code> completely overwrote <code>@69</code>, so the M on +line 3 is actually RAM[42]. To perform this maneuver, we need to make use +of D. + +``` +@69 // set A to 69 +D=M // D is now RAM[69] +@42 // set A to 42 +D;JEQ // if D=0, jump to ROM[42] +``` +</details> + +For convenience, we can attach a label to an instruction in assembly and +reuse it later: + +``` +(END) +@END +0;JMP +``` + +In this code `(END)` points to `@END`, and `JMP` is an unconditional jump, +so this creates an infinite loop. It is good practice to terminate +a program with this, lest the ROM address overflows and the computer runs +the program again from instruction 0. + +You can also use custom symbols after an "@" to assign or reuse +a static address starting from 16. It is like declaring a variable whose +value is stored in RAM[n] where n ≥ 16. Why not 0-15, you ask? Well, they +are reserved for symbols R0-R15. + +This `@symbol` notation goes further by mapping a monochrome screen to +a memory area `@SCREEN`, namely 16384-24575, and a keyboard to `@KBD`, +which is 24576. If you write the highest bit to one in RAM[16384], you +paint the top left pixel black. If you press space, it sets RAM[24576] to +32 (0x20). You can interact with them in the CPU emulator. + + + +▲ CPU Emulator running Pong + +Here's a snippet of HACK assembly I wrote that increments RAM[16] from +0 until it is equal to whatever you put in RAM[0] before running the +program: + +``` +@x +M=0 // x = RAM[16] = 0 + +(LOOP) +@R0 +D=M // D = RAM[0] +@x +D=D-M // D -= x +@END +D;JEQ // if D == 0 goto END +@x +M=M+1 // otherwise x += 1 +@LOOP +0;JMP // goto LOOP + +(END) +@END +0;JMP +``` + +## Project 05: Computer + +After a project that seemed to come out of nowhere, it sounds reassuring +that we're back to building the computer hardware. First we need to decide +the architecture. It is common to build a computer on the Von Neumann +architecture. But canon Von Neumann stores both instructions and data in +a single memory unit, commonly RAM, so the CPU can modify both. But even +so, a tiny ROM is needed to instruct the CPU in its booting process. In +our application however, we will just straightforward use two units simiar +in size. This means given a single ROM, our computer can only run one +specific program. This is called the Harvard architecture, technically +a subset of Von Neumann. AVR microcontrollers also use this architecture. + +So this means there will be three things inside the computer: CPU, ROM, +and RAM. Since we made RAM in project 03 and ROM is builtin, all that's +left is the CPU. + +The CPU needs to: + +- Read instruction from ROM +- Read data from RAM +- Compute something +- Write data to A, D, and RAM +- Run instruction one by one +- Jump to another instruction if programmer asks it to + +The instant I read the requirements, I knew there will be a ton of +internal wires. Fortunately, the authors provided a block diagram similar +to this one: + + + +Yikes! What's with the question marks? Apparently it's the authors' own +version of spoiler alerts. I had to figure out what they are by myself, +and that's a good thing. I like challenges. + +Let's first make sure we know what each pin/chip is doing. + +- Instruction in ROM comes from pin `instruction` +- Data from RAM come from pin `inM` +- Both RAM and ROM addresses are selected using `addressM` +- The ALU takes two registers and churns out an output +- The A and D Register accept inputs from ALU +- ALU output also goes to RAM via `outM` +- `writeM` tells RAM to load data +- The PC increments, resets or jumps to instruction + +What's an instruction anyway? It's a 16-bit value that describes what we +want the CPU to do in this clock cycle. An assembler, which we will write +in project 06, translates assembly to binary code, but in this project +let's assume it came from nowhere. + +What the 16 bits represent depends on the type of instruction you're +writing. It is specified by the highest bit, called the __opcode__. In an +A-instruction, the opcode is 0, which is followed by 15 bits of address. +Considering the size of our larger memory unit, ROM, is 32768 words, 15 +makes sense. In this case the CPU will store the value in the A register. + +The C-instruction with opcode 1 is more complicated, but boils down to +four groups of control bits: + +``` + fixed ALU control jump instruction +\ / \ / \ / ++-----+---+--------+--------+--------+ +| 111 | a | c1..c6 | d1..d3 | j1..j3 | ++-----+---+--------+--------+--------+ + / \ / \ + A/M destination +``` + +- `a` decides whether the ALU takes in D and A, or D and M. +- `c1..c6` correspond to control bits on the ALU. +- `d1..d3` tell CPU to save ALU output to A, D, and M respectively. +- `j1..j3` tell CPU to jump to ROM[A] when ALU output <0, =0, and >0, + respectively. + +In a hunch, it seems we have the answer to most of the question marks. + + + +This is simple but wrong. Let's take a close look at the `load` pin +labeled `d1` on the A register. If we try to load address 1 into it, using +an A-instruction `@1`, what will happen? Let's assemble it: + +``` +0000 0000 0000 0001 +^\________________/ +| ^ +| | +opcode integer value 1 +``` + +The mux on the left will let the instruction through because `opcode` is +0, but remember, HDL doesn't recognize `d1`, it only recognizes +`instruction[5]`. What's gonna happen is, the A register will refuse to +load, because `instruction[5]` is zero. Something similar will also happen +to `d2` and `d3`, so we add a little logic: + + + +This ensures that A, D and M load data if and only if we explicitly tell +them to. Now we shift our attention to the only two question marks left: +`zr` and `ng` coming from the ALU, and `load` going into the PC. + +Notice something? `j1..j3` are missing, so it's definitely them. Recall +that we can set the PC to its input if we pull `load` to high, and this +way we can jump to ROM[A]. But how? + + + +It's actually very straightforward! Apparently the authors thought it +through when specifying the ALU. + + + +(Actual gates may differ) + +And that's it, we made a CPU! We are super close to the computer; all we +need to do is connect all the wires. I'm feeling too tired to sketch up +another diagram so here's the HDL: + +``` +CHIP Computer { + IN reset; + + PARTS: + ROM32K(address=pc, out=instruction); + CPU( + inM=inM, instruction=instruction, reset=reset, + writeM=writeM, outM=outM, addressM=addressM, pc=pc + ); + Memory(in=outM, address=addressM, load=writeM, out=inM); +} +``` + +## Project 06: Assembler + +Having gone through project 04 and 05, if you think something's missing, +then you're right. We haven't talked about how we translate assembly to +binary instructions. In nand2tetris, you are asked to write an assembler +in any high-level language (or not write one at all and assemble by hand). +As the grammar is pretty simple and well-defined, it wouldn't take too +much effort, yes? + +For some reason my self-obsessive ass, after two successful projects in +C (one of them being [SIRTET](../sirtet)), decided to write the assembler +in this very cursed language. + +Roast me all you want, but most of the time I'm thinking about stuff like +"what if the programmer slid in illegal characters in the variable name" +and "hmm so I malloc a piece of memory and strcpy the second to +second-to-last characters from this string. We'll need a null terminator +so the size has to be one byte smaller than the source string blah blah +blah" and I'll take another minute to decide how long this piece of memory +will live until I free it. + +I shall skip the part where I wrote the program because that will bore you +and me to death. Instead, let's watch the results if we assemble the +assembly I showed you in [project 04](#project-04-assembly). The +executable is called `hack-as`, just like `avr-as`. + +``` +$ ./hack-as -v test/inc.asm +====== SYMBOLS ===== +label addr +LOOP 2 +END 12 +x 16 + +====== RESULTS ===== +addr binary inst +0 0000000000010000 @16 +1 1110101010001000 M=0 +2 0000000000000000 @0 +3 1111110000010000 D=M +4 0000000000010000 @16 +5 1111010011010000 D=D-M +6 0000000000001100 @12 +7 1110001100000010 D;JEQ +8 0000000000010000 @16 +9 1111110111001000 M=M+1 +10 0000000000000010 @2 +11 1110101010000111 0;JMP +12 0000000000001100 @12 +13 1110101010000111 0;JMP + +Binary written to test/inc.hack + +$ cat test/inc.hack +0000000000010000 +1110101010001000 +0000000000000000 +1111110000010000 +0000000000010000 +1111010011010000 +0000000000001100 +1110001100000010 +0000000000010000 +1111110111001000 +0000000000000010 +1110101010000111 +0000000000001100 +1110101010000111 +``` + +nand2tetris provided me with a few other assembly files I can test my +assembler against. The longest one was over 28k instructions. All of them +passed. + +As always, I did some memory profiling with valgrind: + +``` +$ valgrind --leak-check=full --show-leak-kinds=all ./hack-as test/inc.asm +==31030== Memcheck, a memory error detector +... +Binary written to test/inc.hack +==31030== +==31030== HEAP SUMMARY: +==31030== in use at exit: 0 bytes in 0 blocks +==31030== total heap usage: 49 allocs, 49 frees, 77,587 bytes allocated +==31030== +==31030== All heap blocks were freed -- no leaks are possible +==31030== +==31030== For lists of detected and suppressed errors, rerun with: -s +==31030== ERROR SUMMARY: 0 errors from 0 contexts (suppressed: 0 from 0) +``` + +(It is indeed weird that it needs 77kB of heap memory, but since we've +been overdoing it all along we might as well just ignore it.) + +The whole process took one night, one day, and one morning. And the +afternoon following that morning, I decided to implement it again using +Python to see how much easier it is. + +The advantage of Python over C is human-oriented string methods like +`str.split` and `str.partition`. Also, no manual memory management. +I finished it in less than an hour, not because Python is easy, but +because I already have C code to refer to. This, in hindsight, is a big +mistake. I should have prototyped it in Python first, _then_ proceed to +write it in C. However the speed benefit C provides is an overkill for +this kind of simple task, so in that case I might just not write C at all. + +And thus we have bridged the gap between assembly language and machine +code. Our computer can run _anything_. (As long as it fits in the ROM) + +## Course review + +### Conceptual + +nand2tetris part 1 takes you on a journey from NAND gates as promised. You +climb a ladder from the humble logic gate to more and more complex chips, +representing increasingly advanced logic, but they're NANDs all the way +down. The authors say that the goal of nand2tetris is to "demystify +computers": Every time you witness the very chip you made do something +exciting, like adding up two numbers or remembering 16 bits of data, one +layer of mystery dissolves, because you _know_ X happens when chip Y does +Z, not because TSMC soaked your wafer in .25 mol/L holy water. +Philosophical takeaway: One complicated thing is just many simple things +arranged in a clever way. + +### Technical + +The project-oriented approach really gets your hands dirty, but not +completely covered in copper particles thanks to its simulators. They are +offered in a software suite, which verifies your work against test scripts +bundled along. This is the best thing of this course. If you grab some +university textbook, the first chapter might be like "OK now go download +NI® Multisim™ for 628 dollars" or "we'll give you an answer to every +question and you just need to convince yourself it works", whereas the +nand2tetris software suite is GPL'd. I only have two points of criticism: + +- It is buggy at times (the safe kind, you just need to restart it) +- It is written in Java (I have a prejudice against everything Java) + +As I mentioned in [Project 02](#project-02-alu), every time you advance into +a new project, all the chips you've made thus far become builtin Java code +instead of HDL. For example, when you simulate the ALU, the +Mux/And16/whatever you're seeing is no longer what you wrote in project +01, but part of the simulator itself. + +Pro: Complex chips run more efficiently and reliably. + +Con: You can't verify your prior chips _actually_ works beyond the test +scripts. + +Of course, the pro beats the con by an order of magnitude. Don't you have +this deep-rooted fear that one loose jumper wire on the breadboard can +knock your Ben Eater-style computer completely off the rail? + + + +▲ Image credit: [Ben Eater, "Build a 6502 computer"](https://eater.net/6502) + +### Course outcome + +The purpose of this course is, in my opinion, to prove to you that +computers are not magic, and that it is _possible_ to build your own +computer. It's like one of those workshops that lets you make a little +bottle opener, but you don't wind up being a blacksmith. That said, the +course does not bother you with the intricacies and technicalities of +real-life engineering. Every step is like playing with Legos, except +there's no microplastic. + +Moreover, there is a very valuable "Perspective" unit at the end of each +project where the instructors, Nisan and Shocken, sit together and explain +something that's technically outside the scope of this course, but good to +know nonetheless. For example, how NAND gates are made in CMOS logic and +how D flip-flops are made from NANDs. This opens up a whole new door if +you happen to be interested. + +To make my own computer almost from scratch is a greatly pleasant +experience. I would definitely recommend this course. |
