Project Summary - Nand2Tetris

Link of interest

• nand2tetris.org

Introduction

• we are learning 3 things:
  1. how computers work,
  2. how to break complex problems into manageable modules,
  3. how to develop large-scale hardware and software systems.
• how codes work:
  1. write C sourcecode in file
  2. file is compiled into machine-level codes
  3. machine-level codes (binary code-map) are executed by a chipset -- register, memory, ALU.
  4. all the hardware stuff in 3. >> they are all logic-gates.
• abstractions - we use it to "split off" complex projects into simple parts, as we did here.

Lesson 01: Boolean and Logic Gates

• Basic boolean building blocks are NOT & AND
  • OR(X,Y) can be construct with NOT(AND(X,Y))
• we can further discard NOT & AND by just using NAND Logic:
  • NOT X = NAND(X,X)
  • X OR Y = NAND(NAND(X,X),NAND(Y,Y))
  • X AND Y = NAND(NAND(X,Y),NAND(X,Y))
  • Trivia: NOR can do these too. we call them "universal gates"
• With these we can build up complex functions
• For logic gates, we start with truth table work backwards to construct functions that can implement addition and multiplication etc.
• We start with having an input of 1-bit. However, later on we will have more bit (16-bits etc.) to manipulate. It is better to thing of them as one group -- "bus" (latin for "many")
• Building up from NANDs, the basic blocks are NOT,AND,OR,XOR,MUX,DMUX. (can be many-bits version).
• Mux and Demux is useful when shared communication over a single line. (selecting by feeding certain frequencies to the "select" channel of Mux/Demux)
• We can do 3-way or more combining inputs by cumulatively applying the basic blocks. for DMUX, it's similar to branching out and vice versa for MUX.

Lesson 02: Boolean Arithmetic and ALU

• How to convert from decimal to binary
  • find the biggest "buckets" that decimal number can fit then down to the next biggest one.
  • Example, 99 is 64 + 32 + 0 + 0 + 0 + 2 + 1
  • Therefore, in binary form, it is 1100011
• The following are the basic arithmetics we want to have: Add, Subtract, which is greater, Multiply, Divide
• First we will get "Add", then we get "Subtract" and "which is greater" for free
  • "Subtract" is adding another negative number together (this depends on how to represent negative numbers in a clever way)
  • "Greater" means we can subtract the two numbers and see whether result is positive.
• How to build Multi-bits Adder
  1. Build Half-Adder --> input a,b and output a sum and carry (called H-carry)
  2. Build Full-Adder --> input a,b,H-carry then output "true sum" and "true carry"
  3. Build multi-bits Adder by stacking the Full-Adder cumulatively -- digits by digits
• About "ALU" inside a cpu
  • generally used to compute integer and logic stuff. other computation can be implemented later in software.
  • in "Hack ALU" design, there are 2 16-bit inputs, 1 function select, and 1 16-bit output

Lesson 03: Memory

• Why do we need memory?
  • for loop, memory "states", counters
  • deal with physical speed - the gap in one discrete "clock" cycle to make sure all electrical/transistor input/output changes are done before one ticks.
• Types of logic
  • combinatorial: out[t] = func(in[t])
  • sequential: out[t+1] = func(in[t])
• How to implement states?
  • in[t+1] = func(in[t]) .. AKA Flip-Flop unit (func = identity).
• Register is a multi-bit register chained together
  • WORD = width of the register
• RAM (our actual memory unit)
  • stores both data and code to run. remember von neumann...
  • this is just a bunch of registers stacked together
  • select register to manipulate by setting "address" and turn on "load" flag
• Counter
  • need this so that we could fetch the code and execute them one by one
  • counter interface: RESET, NEXT, GOTO