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机缘巧合，有机会可以学习这门课。问题是自己的毅力实在不足从九月份到十二月份重置了无数次，才看到第二周。今年给自己的打分绝对是1分。

From Nand to Tetris是希伯来大学的一门网络课程。选择这门课的初衷是因为毕竟从事通信行业，想要从更底层了解一下计算机。事实证明它也确实很有用，L1物理层就需要了解HDL编程。

Week1 Overview

Hello, World Below

课程目的

1. 计算机如何工作
2. 如何将复杂问题分解为易于管理的模块
3. 如何开发大规模硬件和软件系统

向下通往硬件领地之路

任何程序在实际运行之前，首先必须被翻译成某种目标计算机平台的机器语言。其编译过程可被划分为若干个抽象层级：

• 编译器
• 虚拟机
• 汇编编译器

从概念上可分为两个阶段

• 语法分析 syntax analysis: 对源文本进行分析，分组成有意义的语言结构，保存到parse tree
• 代码生成 code generation

Boolean Logic

布尔代数 Boolean Algebra

布尔代数处理布尔型数值(true/false, 0/1 …)。

Specification

NAND

全1为0， 此课程中认为NAND是最基本的单元不需要实现

芯片名: Nand

输 入: a, b

输 出: out

功 能: If a=b=1 then out=0 else out=1

说 明: 基本门，不需实现

Basic Logic Gates

NOT

单输入变量的NOT gate, 也成为converter

芯片名: Not

输 入: in

输 出: out

功 能: If in=0 then out=1 else out=0

实现：NAND(a,a)

CHIP Not {
    IN in;
    OUT out;

    PARTS:
    Nand(a = in, b = in, out = out);
}

AND

只有当输入都是1时，输出1

芯片名: And

输 入: a, b

输 出: out

功 能: If a=b=1 then out=1 else out=0

实现：NOT(NAND(a,b)

CHIP And {
    IN a, b;
    OUT out;

    PARTS:
    // Put your code here:
    Nand(a=a, b=b, out=outNand);
    Not(in=outNand, out = out);
}

OR

有1为1

芯片名: Or

输 入: a, b

输 出: out

功 能: If a=b=0 then out=0 else out=1

实现：NAND(NAND(a,a),NAND(b,b))

CHIP Or {
    IN a, b;
    OUT out;

    PARTS:
    // Put your code here:
    Nand(a = a, b = a, out = aNand);
    Nand(a = b, b = b, out = bNand);
    Nand(a = aNand, b = bNand, out = out);
}

Xor 异或

即异或，相同为0，不同为1

芯片名: Xor

输 入: a, b

输 出: out

功 能: If a!=b then out=1 else out=0

实现：out = not (a == b) = And(Or(a, b), Nand(a,b))

CHIP Xor {
    IN a, b;
    OUT out;

    PARTS:
    // Put your code here:
    Or(a = a, b = b, out = abOr);
    Nand(a = a, b = b, out = abNand);
    And(a = abOr, b = abNand, out = out);
}

Multiplexor 选择器

三输入变量的门电路。

芯片名: Mux

输 入: a, b, sel

输 出: out

功 能: If sel = 0 then out=a else out=b

实现：[a and b] or [a and not(b) and not(c)] or [not(a) and b and c]

CHIP Mux {
    IN a, b, sel;
    OUT out;

    PARTS:
    Not(in = a , out = aNot);
    Not(in = b, out = bNot);
    Not(in = sel, out = selNot);
    And(a = a, b = b, out = aAndb);
    And(a = a, b = bNot, out = aAndnotb);
    And (a = aAndnotb, b = selNot, out = aAndnotbAndnotsel);
    And (a = aNot, b = b, out = notaAndb);
    And (a = notaAndb, b = sel, out = notaAndbAndsel);
    Or (a = aAndb, b = aAndnotbAndnotsel, out = out1);
    Or(a = out1, b = notaAndbAndsel, out = out);
}

Demultiplexor

与Mux相反,只有一个输入变量，有两个输出

芯片名: DMux

输 入: in, sel

输 出: out

功 能: If sel = 0 then (a=in, b=0) else (a=0, b=in)

实现： a = in and not(sel), b = in and sel

CHIP DMux {
    IN in, sel;
    OUT a, b;

    PARTS:
    // Put your code here:
    // a = in and not(sel) 
    // b = in and sel
    Not(in = sel, out = notSel);
    And(a = in, b = notSel, out = a);
    And(a = in, b = sel, out = b);
}

Multi-Bit Versions of Basic Gates 多位基本门

通用计算机的设计要求其能够在多为数据线上运行

• Multi-Bit Not 对它的n位输入总线上的每一位取反

芯片名: Not16

输 入: in[16]

输 出: out[16]

功 能: For i=0..15 out[i]=Not(in[i])

• Multi-Bit And And16.hdl

16-bit bitwise And:

for i = 0..15: out[i] = (a[i] and b[i])

• Multi-Bit Or Or16.hdl

• Multi-Bit Multiplexor Mux16.hdl

Multi-Way Versions of Basic Gates 多通道逻辑门

即将2位逻辑门推广到多位

Multi-Way Or

对于一个n位的Or门， 当n位输入变量中任意一位或以上为1，输出为1，否则为0

8-way Or:

out = (in[0] or in[1] or … or in[7])

Or8Way.hdl

Multi-Way/Multi-Bit Multiplexor

一个拥有m个通道，每个通道数据宽度为n位的multiplexor选择器

4-way 16-bit multiplexor:

out = a if sel == 00

​ b if sel == 01

​ c if sel == 10

​ d if sel == 11

实现：机器语言是从低位到高位处理的 因此 Mux4Way16.hdl

• Mux16(a=a, b=b, sel=sel[0], out=aa);

• Mux16(a=c, b=d, sel=sel[0], out=bb);

• Mux16(a=aa, b=bb, sel=sel[1], out=out);

Multi-Way/Multi-Bit Demultiplexor

m通道n位的demultiplexor从m个可能的n位输出通道中选择输出一个n位的输入变量

4-way demultiplexor:

{a, b, c, d} = {in, 0, 0, 0} if sel == 00

​ {0, in, 0, 0} if sel == 01

​ {0, 0, in, 0} if sel == 10

​ {0, 0, 0, in} if sel == 11

实现：太费脑子了 想不明白 怎么想出来的： 就是看哪一位有1

• DMux(in=in, sel=sel[1], a=aa, b=bb);

• DMux(in=aa, sel=sel[0], a=a, b=b);

• DMux(in=bb, sel=sel[0], a=a, b=b);