Notes for Nand2Tetris: Computer Architecture

This is a note for Nand2Tetris Unit 5.

Unit 5.1

Same Hardware can run many different Software programs.

• Theory: Universal Turing Machine
• Practice: Von Neumann Architecture

Memory stores Data and Program. CPU is composed of ALU and Registers.


Registers store both Data and Addresses.

Unit 5.2

The Fetch-Execute Cycle

The basic CPU loop

• Fetch an instruction from the Program memory
• Execute it

Fetching

• Put the location of the next instruction into the "address" of the program memory
• Get the instruction code itself by reading the memory contents at that location

Use program counter.

Executing

...

Fetch-Execute Clash


How to solve that? Do one after the other (Use Mux).

Solution: Mux and Instruction register


Simpler solution: Harvard Architecture

• Variant of Von Neumann Architecture
• Keep Program and Data in two separate memory modules
• Complication avoided

Unit 5.3

Abstraction of the Hack CPU

A 16-bit processor, designed to:

• Execute the current instruction
• Figure out which instruction to execute next (instructions written in the Hack language)

The overall computer architecture


Hack CPU Interface



Hack CPU Implementation


Instruction handling

When handling A-instruction (op-code is 0), the Mux16 takes the input from instruction, while handling C-instruction (op-code is 1), it should be from the output of ALU.

CPU handling of an A-instruction:

• Decodes the instruction into op-code + 15-bit value
• Stores the value in the A-register
• Outputs the value

CPU handling of a C-instruction:

• Decodes the instruction into four parts (op-code, ALU control bits, Destination load bits and Jump bits)
• ...

ALU operation

ALU data inputs:

• From the D-register
• From the A-register / M-register

ALU control inputs:

• Control bits (from the instruction)

ALU data output:

• Result of AlU calculation, fed simultaneously to: D-register, A-register, M-register
• Which register actually received the incoming value is determined by the instructions' destination bits

ALU control outputs:

• Negative output?
• Zero output?

Jump

Program Counter abstraction:

Emits the address of the next instruction:

To start / restart the program's execution: PC=0

• no jump: PC++
• goto: PC=A
• conditional goto: if the condition is true PC=A else PC++

PC logic:

if reset==1:
    PC=0
else:
    # current instruction
    load = f(jump_bits, ALU_control_outputs) # the load bit of PC
    if load==1:
        PC=A
    else:
        PC=PC+1

Unit 5.4

Hack CPU Operation

Sample Hack instructions:

D=D-A
@17
M=M+1

The CPU executes the instruction according to the Hack language specification:

• If the instruction includes D and A, the respective values are read from, and/or written to, the CPU-resident D-register and A-register;
• If the instruction is @x, then x is stored in the A-register; this value is emitted by addressM
• If the instruction's RHS includes M, this value is read from inM
• If the instruction's LHS includes M, then the ALU output is emitted by outM, and the writeM bit is asserted

@100
D=D-1;JEQ

If (reset==0):

The CPU logic uses the instruction's jump bits and the ALU's output to decide if there should be a jump.

• If there is a jump: PC is set to the value of the A-register
• Else (no jump): PC++

The updated PC value is emitted by pc

If (reset==1):

PC is set to 0, pc emits 0 (causing a program restart)

Memory

We divide the memory to three segments.

Abstraction:

• Address 0 to 16383: data memory
• Address 16384 to 24575: screen memory map
• Address 24576: keyboard memory map

Implementation:

• RAM: 16-bit / 16K RAM chip
• Screen: 16-bit / 8K memory chip with a raster display (光栅显示) side-effect
• Keyboard: 16-bit register with a keyboard side-effect

Screen:

To turn pixel(row, col) on/off: $w=Screen(row\times32+col\div16)$

In the Hack Memory context: $w=Memory[16384+row\times32+col\div16]$. Set the $col % 16$ bit of $w$ to 1 or to 0.

Keyboard:

To read the keyboard:

• Probe the output of the Keyboard register
• In the Hack Memory context: probe memory register 24576

Instruction Memory (ROM)

To run a program on the Hack computer:

• Load the program into the ROM
• Press "reset"
• The program starts running

Hardware implementation: plug-and-play ROM chips

Hardware simulation: programs are stored in text files; program loading is emulated by the built-in ROM chip

Hack Computer implementation


Unit 5.5

...

Project 5

CPU.hdl

吐槽：一开始我想的是，连设计图都给我了，我还能做不出来吗？前人已经载好了树，我这乘凉还不容易吗？实际上手才发现，CPU 不愧是 CPU，即使是这样一个非常简化的版本，也是相当复杂的。这凉，还真不是那么好乘。:x

记录一下制作这个 CPU 的思考过程：

首先，按照设计图，把 ALU、ARegister、DRegister、PC 和两个 Mux16 摆出来；

接着，接线，把一些能连起来的 PIN 口连起来，为了搞清楚输入输出，我在图上将变量名都标出了（例如 ALU output 标记为 aluo，A Register 的输出标记为 ao 等等）；

最后，最复杂的一步，填入 control bits（包括 sel bits, load bits 等等）。


在构造这些 control bits 之前，我们需要明确：这个 CPU 将处理 A-instruction 和 C-instruction 两类指令，这意味着 control bits 与指令类型有关。并且，分析这两类指令可以发现：

• A-instruction 必然改变并且只改变 ARegister 的值；
• C-instruction 可以改变 ARegister、DRegister、M Register 和 PC 的值，具体是否改变取决于 instruction。

明确这点后，让我们来构造第一个 control bit: 第一个 Mux16 的 sel。这个 Mux16 接受 instruction 和 ALU output，并且将结果（我这里的标记是 mo1，Mux output 1）传给 ARegister。Unit 5.3 Instruction handling 部分说的很清楚，当处理 op-code（也就是 instruction [15]）是 0 的 A-instruction 时，这个 Mux16 读入 instruction，否则，读入 ALU output。所以，我们的一号 Mux16 长这样：

Mux16(a=instruction, b=aluo, sel=instruction[15], out=mo1); // Mux 1

我构造的第二个 control bit 是第二个 Mux16 的 sel。观察指令表的 comp 部分，可以发现：指令中的 a=0 和 a=1（这个 a 也就是 instruction [12]）决定了传入 ALU 的是 A 还是 M，这与这二号 Mux16 的接线相符合。所以，二号 Mux16 长这样：

Mux16(a=ao, b=inM, sel=instruction[12], out=mo2); // Mux 2

接下来来构造 ARegister 的 load bit，DRegister 的 load bit 和 控制 writeM 的这三个 control bits。其中 writeM 其实就是控制是否写入内存的 control bit，也就是控制 M Register 的 load bit。观察指令表的 dest 部分，我们可以发现 d1 (instruction [5])，d2 (instruction [4])，d3 (instruction [3]) 分别控制着是否写入 ARegister，是否写入 DRegister 和是否写入 MRegister（也就是 writeM 是否为真）。所以这三个 control bits 是不是就分别是 instruction [5]，instruction [4] 和 instruction [3] 呢？一开始我就是这么想的，但是，回想前面分析过的两类 instructions 的区别，只有当指令是 C-instruction 时，instruction [5]、[4]、[3] 才分别是 d1、d2、d3（A-instruction 时这几个 bits 都只是 地址的一部分嘛）。所以，这三个 control bits 还需要一些加工：

• 当且仅当指令是 A-instruction 或标记了写入 ARegister 的 C-instruction 时，loadA 为真
• 当且仅当指令为标记了写入 DRegister 的 C-instruction 时，loadD 为真
• 当且仅当指令为标记了写入 MRegister 的 C-instruction 时，writeM 为真

// loadA (a-instruction or c-instruction)
Not(in=instruction[15], out=ainst); // ainst: a-instruction
Or(a=instruction[5], b=ainst, out=loadA);
// loadD (c-instruction)
And(a=instruction[4], b=instruction[15], out=loadD);
// writeM (c-instruction)
And(a=instruction[3], b=instruction[15], out=writeM);

然后让我们来构建 ALU 的 zx, nx, zy, ny, f, no 这几个 control bits。判断的方法应该是观察指令表的 comp 部分。这里其实我只判断了 c5 (instruction [7])、c6 (instruction [6]) 分别表示 f 和 no，然后猜测了一下前面的 c1 到 c4 分别表示 zx、nx、zy、ny。这样，ALU 长这样（注意这里的 zr、ng，后边有大用场）：

ALU(x=do, y=mo2,
    zx=instruction[11], nx=instruction[10],
    zy=instruction[9], ny=instruction[8],
    f=instruction[7], no=instruction[6],
    out=aluo, out=outM, zr=zr, ng=ng);

最后是 PC 的 control bit。这个 control bit 我觉得是最复杂的一个。回顾 Unit 5.3 Jump 部分，我们可以看到，这个 control bit（我把它叫做 loadPC）由 jump_bits 和 ALU_control_outputs 共同决定：

load = f(jump_bits, ALU_control_outputs) # the load bit of PC

jump_bits 指的就是 j1、j2、j3，也就是 instruction [2]、instruction [1]、instruction [0]；ALU_control_outputs 也就是 zr、ng。

观察指令表的 jump 部分，可以发现：j1、j2、j3 分别为真就分别表示这条指令要求 comp 部分指令的结果（也就是 ALU output）分别满足 <0, =0 和>0。如何判断 ALU output 是否满足 <0、=0、>0 呢？zr、ng 就派上了用场，它们就分别表示 =0 和 <0，而表示 >0 的 ps（positive 的简写）则可以用 zr 和 ng 构造：ps = NOT(ng OR zr) = NOT(zr) and NOT(ng)。将 ng, zr, ps 分别与 j1, j2, j3 进行与操作，就可以得出计算结果是否满足指令要求的 <0、=0、>0 了，将这些与的结果（jlt、jeq、jgt）两两拼接，就可以得到 jle、jne、jge 了。不跳跃就是永假，无条件跳跃的 jmp 则是三路或运算，可以使用 Or8Way 中的前三路进行，后边用不到的全部置为 false 就行了：

// null: false
And(a=ps, b=instruction[0], out=jgt);
And(a=zr, b=instruction[1], out=jeq);
And(a=ng, b=instruction[2], out=jlt);
Or(a=jgt, b=jeq, out=jge); // great than OR equal to
Or(a=jgt, b=jlt, out=jne); // great than OR less than
Or(a=jeq, b=jlt, out=jle); // less than OR equal to
// jmp:
Or8Way(in[0]=jgt, in[1]=jeq, in[2]=jlt, in[3..7]=false, out=jmp);

最后，只要这 8 个中的任一个为真（当然第一个不跳跃为永假，所以事实上其实是后 7 个中的任一个为真），那就是要跳跃的（jump 为真）。但 jump 还不是最后的 loadPC —— 当且仅当指令是 C-instruction 时，jump 才是 loadPC。而 inc 则与 loadPC 的真值相反，因为不跳跃的话，就是执行下一条指令嘛：

// jump or increase
Or8Way(in[0]=false, in[1]=jgt, in[2]=jeq, in[3]=jge,
        in[4]=jlt, in[5]=jne, in[6]=jle, in[7]=jmp, out=jump);
// loadPC (c-instruction)
And(a=jump, b=instruction[15], out=loadPC);
Not(in=loadPC, out=increase);

最后，完整的代码如下：

/**
 * The Hack CPU (Central Processing unit), consisting of an ALU,
 * two registers named A and D, and a program counter named PC.
 * The CPU is designed to fetch and execute instructions written in
 * the Hack machine language. In particular, functions as follows:
 * Executes the inputted instruction according to the Hack machine
 * language specification. The D and A in the language specification
 * refer to CPU-resident registers, while M refers to the external
 * memory location addressed by A, i.e. to Memory[A]. The inM input
 * holds the value of this location. If the current instruction needs
 * to write a value to M, the value is placed in outM, the address
 * of the target location is placed in the addressM output, and the
 * writeM control bit is asserted. (When writeM==0, any value may
 * appear in outM). The outM and writeM outputs are combinational:
 * they are affected instantaneously by the execution of the current
 * instruction. The addressM and pc outputs are clocked: although they
 * are affected by the execution of the current instruction, they commit
 * to their new values only in the next time step. If reset==1 then the
 * CPU jumps to address 0 (i.e. pc is set to 0 in next time step) rather
 * than to the address resulting from executing the current instruction.
 */

CHIP CPU {
    IN  inM[16],         // M value input  (M = contents of RAM[A])
        instruction[16], // Instruction for execution
        reset;           // Signals whether to re-start the current
                         // program (reset==1) or continue executing
                         // the current program (reset==0).

    OUT outM[16],        // M value output
        writeM,          // Write to M?
        addressM[15],    // Address in data memory (of M)
        pc[15];          // address of next instruction

    PARTS:
    ALU(x=do, y=mo2,
        zx=instruction[11], nx=instruction[10],
        zy=instruction[9], ny=instruction[8],
        f=instruction[7], no=instruction[6],
        out=aluo, out=outM, zr=zr, ng=ng);
    ARegister(in=mo1, load=loadA, out=ao, out[0..14]=addressM);
    DRegister(in=aluo, load=loadD, out=do);
    PC(in=ao, load=loadPC, inc=increase, reset=reset, out[0..14]=pc);

    Mux16(a=instruction, b=aluo, sel=instruction[15], out=mo1); // Mux 1
    Mux16(a=ao, b=inM, sel=instruction[12], out=mo2); // Mux 2

    // loadA (a-instruction or c-instruction)
    Not(in=instruction[15], out=ainst); // ainst: a-instruction
    Or(a=instruction[5], b=ainst, out=loadA);
    // loadD (c-instruction)
    And(a=instruction[4], b=instruction[15], out=loadD);
    // writeM (c-instruction)
    And(a=instruction[3], b=instruction[15], out=writeM);

    // use `zr` and `ng` to implement conditional jump
    // make a `ps` (positive)
    Not(in=ng, out=notng);
    Not(in=zr, out=notzr);
    And(a=notng, b=notzr, out=ps);

    // null: false
    And(a=ps, b=instruction[0], out=jgt);
    And(a=zr, b=instruction[1], out=jeq);
    And(a=ng, b=instruction[2], out=jlt);
    Or(a=jgt, b=jeq, out=jge); // great than OR equal to
    Or(a=jgt, b=jlt, out=jne); // great than OR less than
    Or(a=jeq, b=jlt, out=jle); // less than OR equal to
    // jmp:
    Or8Way(in[0]=jgt, in[1]=jeq, in[2]=jlt, in[3..7]=false, out=jmp);

    // jump or increase
    Or8Way(in[0]=false, in[1]=jgt, in[2]=jeq, in[3]=jge,
           in[4]=jlt, in[5]=jne, in[6]=jle, in[7]=jmp, out=jump);
    // loadPC (c-instruction)
    And(a=jump, b=instruction[15], out=loadPC);
    Not(in=loadPC, out=increase);
}

Memory.hdl

核心思想：内存的前几位决定了这片内存是 RAM16K、Screen 还是 Keyboard。

/**
 * The complete address space of the Hack computer's memory,
 * including RAM and memory-mapped I/O.
 * The chip facilitates read and write operations, as follows:
 *     Read:  out(t) = Memory[address(t)](t)
 *     Write: if load(t-1) then Memory[address(t-1)](t) = in(t-1)
 * In words: the chip always outputs the value stored at the memory
 * location specified by address. If load==1, the in value is loaded
 * into the memory location specified by address. This value becomes
 * available through the out output from the next time step onward.
 * Address space rules:
 * Only the upper 16K+8K+1 words of the Memory chip are used.
 * Access to address>0x6000 is invalid. Access to any address in
 * the range 0x4000-0x5FFF results in accessing the screen memory
 * map. Access to address 0x6000 results in accessing the keyboard
 * memory map. The behavior in these addresses is described in the
 * Screen and Keyboard chip specifications given in the book.
 */

CHIP Memory {
    IN in[16], load, address[15];
    OUT out[16];

    PARTS:
    DMux4Way(in=load, sel=address[13..14], a=loadram1, b=loadram2, c=loadscr, d=loadkbd);
    Or(a=loadram1, b=loadram2, out=loadram);
    RAM16K(in=in, load=loadram, address=address[0..13], out=ramo);
    Screen(in=in, load=loadscr, address=address[0..12], out=scro);
    Keyboard(out=kbdo);
    Mux4Way16(a=ramo, b=ramo, c=scro, d=kbdo, sel=address[13..14], out=out);
}

Computer.hdl

Just follow the diagram.

/**
 * The HACK computer, including CPU, ROM and RAM.
 * When reset is 0, the program stored in the computer's ROM executes.
 * When reset is 1, the execution of the program restarts.
 * Thus, to start a program's execution, reset must be pushed "up" (1)
 * and "down" (0). From this point onward the user is at the mercy of
 * the software. In particular, depending on the program's code, the
 * screen may show some output and the user may be able to interact
 * with the computer via the keyboard.
 */

CHIP Computer {
    IN reset;

    PARTS:
    ROM32K(address=pco, out=next);
    // memory output, ... , outM output, writeM output, addressM output, pc output
    CPU(inM=memo, instruction=next, reset=reset, outM=outmo, writeM=writemo, addressM=addrmo, pc=pco);
    Memory(in=outmo, load=writemo, address=addrmo, out=memo);
}