let's build a computer - zenspider.comryan/presentations/2014_gogaruco_lets_build… ·...

Year3014

After aseries ofdemotions

Sous-Chef3

Assistant

ISSIcarus

UnfortunateAccident

PhaseMatter Array

Dark MatterCephalopod

Killing8

TheCaptain

ScienceOfficer

Engineer11

and, ofcourse

TheComputer

I’mstranded!

All IHave

PowerSupply

A Bucket ofNAND gates

andthisbook

I am...19

Lost In Space

Ryan Davis, Seattle.rbLet’s Build a Computer!

@the_zenspiderGoGaRuCo 3014

Let’s Build a Computer!

Setting ExpectationsHighly Technical Talk

(I hope) Highly Approachable Talk

200 Slides ≅ 6 ⅔ spm

I have to go incredibly fast.

Not my field of expertise at all. I’m terrified.22

Nand to Tetris

this book24

@the_zenspiderGoGaRuCo 3014 25

High Level Language & OS

Virtual Machine

Assembly Language

Machine Language

Hardware Platform

Chips & Logic Gates

Physics

Virtual Machine

Assembly Language

Machine Language

Hardware Platform

Chips & Logic Gates

Physics

Virtual Machine

Assembly Language

Machine Language

Hardware Platform

Chips & Logic Gates

Physics

@the_zenspiderGoGaRuCo 3014 26statement of the system’s abstraction—namely, the various services that it isexpected to deliver. Having presented the what, each chapter proceeds to discuss howthe abstraction can be implemented, leading to a (proposed) Implementation section.The next section is always Perspective, in which we highlight noteworthy issues leftout from the chapter. Each chapter ends with a Project section that provides step-by-step building instructions, testing materials, and software tools for actually buildingand unit-testing the system described in the chapter.

Projects

The computer system described in the book is for real—it can actually be built, andit works! A reader who takes the time and effort to gradually build this computer willgain a level of intimate understanding unmatched by mere reading. Hence, the bookis geared toward active readers who are willing to roll up their sleeves and build acomputer from the ground up.

Each chapter includes a complete description of a stand-alone hardware or soft-ware development project. The four projects that construct the computer platformare built using a simple Hardware Description Language (HDL) and simulated on ahardware simulator supplied with the book. Five of the subsequent software projects

Typicalsoftwarehierarchy

Typicalhardwareplatform

High-Level Language / Applications (∞)

Operating System

Compiler

Virtual Machine

Assembler

Computer Architecture

Machine Language

ALU Memory Elements

Boolean Arithmetic

Boolean Logic

Sequential Logic

Figure P.1 Book and proposed course map, with chapter numbers in circles.

xii Preface

From “Elements of Computing Systems”

Projects

Operating System

Compiler

Virtual Machine

Assembler

Machine Language

ALU Memory Elements

Boolean Arithmetic

Boolean Logic

Sequential Logic

xii Preface

Projects

Operating System

Compiler

Virtual Machine

Assembler

Machine Language

ALU Memory Elements

Boolean Arithmetic

Boolean Logic

Sequential Logic

xii Preface

Complexity builds from Simplicity

Boolean Logic

Boolean Arithmetic

Sequential Logic

Computer Logic

Very Important:

This is NOT comic sans!

ttttt Hand-drawn font called Sketchnote!

Boolean Logic

WTF is a

Nand?!?32

Not-And

Nand34

a b nand

Rubydef nand a, b ! (a && b) end

Rubyclass Object def ⅋⅋ other ! (self && other) end end

So Cool!

Universal Gates

Xor / Mux / Dmux

Only using ?

Nand →

Not?42

a b nand

Nand →

a b nand

Only using & ?

NOT NAND

a b and

nand →

and?48

a b nand

not nand

a b nand

not not and

a b nand

not not and

a b nand

NAND NOT nand-not

a b and

NAND NAND

a b and

Only using , , & ?

a b or

De Morgan’s Law!

Venn Diagrams??!!

@the_zenspiderGoGaRuCo 3014http://en.wikipedia.org/wiki/Venn_diagram

Venn Diagrams??!!

Venn Diagrams!

http://thisisindexed.com/

Venn Diagrams!

!(A | B)

(!A & !B)

!(!A & !B)

!(!A & !B) = A | B

a | b67

a b or

!(!a & !b)

a b or

AND NOT

not(and( not(a), not(b)))

a b or

AND NOT

not(and( not(a), not(b)))

a b or

AND NOT

NOT nand( not(a), not(b))

a b or

NOT nand( not(a), not(b))

a b or

nand( nand(a,a), nand(b,b))

a b or

NANDNAND

Only using , ,

NOT NAND

a b xor

a & !b | !a & b

a b xor

a & !b | !a & b

a b xor

a & !b | !a & b

a b xor

a & !b | !a & b

a b xor

a & !b | !a & b

NAND NAND

a b xor

a & !b | !a & b

NAND NAND

a b xor

a & !b | !a & b

NAND NAND

a b xor

a & !b | !a & b

a b xor

a & !b | !a & b

a b xor

a & !b | !a & b

a b xor

Muxes are Easy!mux = if sel then b else a end

Just an if

stateme

sel a b xorT T T TT T F FT F T TT F F FF T T TF T F TF F T FF F F F

DMuxes are easy, kindaif sel then a = in else b = in end

dmux94

sel in a b

T T T F

T F F F

F T F T

F F F F

dmux95

sel in a b

T T T F

T F F F

F T F T

F F F F

dmux96

NAND NAND

sel in a b

T T T F

T F F F

F T F T

F F F F

N-way Gates

or8way

or8waydef or8way a,b,c,d,e,f,g,h a || b || c || d || e || f || g || h end

h 1 output

tsdepth/tim

1 output

depth/time

mux4way

2 bit selector

mux8way

3 bit selector

mux8way

dmux4way

2 bit selector

dmux8way

3 bit selector

“Trivial”107

Exercise for the

“Reader”108

Just Remember

16 Bit Logic & More

“Trivial”116

Exercise for the Reader

Boolean Arithmetic

Adders!

Not these Adders

https://www.flickr.com/photos/79818573@N04/14226945188

Nor Black Adder

Just Good, Simple,

Arithmetic!122

Adders, Elementary-School Style

11 +012

11 +01

Adders

11 +01

half adder

11 +01

Adders

full adder

Half Adder

XOR Sum

Full Adder

XOR XOR

16-bit Adder

FullAdder

But Ryan!130

Doesn’t this have the same problem as or8way?

Why, Yes!132

Yes, it does!

What they don’t teach you in grade school…

Full Adder

XOR XOR

Full Adder?

XOR XOR

Propagate

Generate

Partial Full Adder

S0S1S2S3P0P1P2P3

G0G1G2G3PFA

S0-3S4-7S8-11S12-15P0P1P2P3

G0G1G2G3add4

A0-3 B0-3

A4-7 B4-7

A8-11 B8-11

A12-15 B12-15

Carry Lookahead Monster

cla2 (1

p1x1g2x1

c3x1c2x1

p0x1g0x1

p2x1c0x1

g3x1g1x1

Slightly Less Scary? (define (cla g0 g1 g2 g3 p0 p1 p2 p3 cin c1 c2 c3 pout gout) (let-values ([(w1c0 w1c1 w1c2) (wires w 3)] [(w2c1 w2c2) (wires w 2)] [(w3c2) (w)] [(w1g w2g w3g) (wires w 3)]) (append (list (comment (comment-cla))) (And p0 cin w1c0) (Or g0 w1c0 c1) ! (And p1 g0 w1c1) (and3 p1 p0 cin w2c1) (or3 g1 w1c1 w2c1 c2) ! (And p2 g1 w1c2) (and3 p2 p1 g0 w2c2) (and4 p2 p1 p0 cin w3c2) (or4 g2 w1c2 w2c2 w3c2 c3) ! (And p3 g2 w1g) (and3 p3 p2 g1 w2g) (and4 p3 p2 p1 g0 w3g) ! (or4 g3 w1g w2g w3g gout) (and4 p3 p2 p1 p0 pout))))

No, not really.

Least Scary, Most Abstract

Ci = Gi + PiCi-1 Gi = AiBi Pi = Ai + Bi

Least Scary, Most Abstract

Ci = Gi + PiCi-1 Gi = AiBi Pi = Ai + Bi

Least Scary, Most Concrete

C1 = G0 + P0C0 C2 = G1 + P1G0 + P1P0C0 C3 = G2 + P2G1 + P2P1G0 + P2P1P0C0 C4 = G3 + P3P2G1 + P3P2P1G0 + P3P2P1P0C0

Least Scary, Most Concrete

C1 = G0 + P0C0 C2 = G1 + P1G0 + P1P0C0 C3 = G2 + P2G1 + P2P1G0 + P2P1P0C0 C4 = G3 + P3P2G1 + P3P2P1G0 + P3P2P1P0C0

I can handle that…

Just Details

Incrementers

Half Adder

o12…

Faster, but Scarier

��

http://www.righto.com/2013/11/the-z-80s-16-bit-incrementdecrement.html

Arithmetic Logic Unit

f(x,y)ALU

zx zynx ny f no

f(x,y)ALU

zx zynx ny f no

f(x,y)ALU

zx zynx ny f no

f(x,y)ALU

zx zynx ny f no

f(x,y)ALU

zx zynx ny f no

Arithmetic Logic UnitIN x[16], y[16], // 16-bit inputs zx, // zero the x input? nx, // negate the x input? zy, // zero the y input? ny, // negate the y input? f, // compute out = x+y (f=1) else x&y no; // negate the out output? !OUT out[16], // 16-bit output zr, // 1 if (out == 0), 0 otherwise ng; // 1 if (out < 0), 0 otherwise

Arithmetic Logic UnitMux16(a=x, b=false, sel=zx, out=x2); Mux16(a=y, b=false, sel=zy, out=y2); !Not16(in=x2, out=notx2); // if (zx==1) set x = 0 Not16(in=y2, out=noty2); // if (zy==1) set y = 0 !Mux16(a=x2, b=notx2, sel=nx, out=x3); // if (nx==1) set x = ~x Mux16(a=y2, b=noty2, sel=ny, out=y3); // if (ny==1) set y = ~y !Add16(a=x3, b=y3, out=add16); // if (f==1) set out = x + y And16(a=x3, b=y3, out=and16); // if (f==0) set out = x & y Mux16(a=and16, b=add16, sel=f, out=out1); !Not16(in=out1, out=notout); Mux16(a=out1, b=notout, sel=no, out=out, // if (no==1) set out = ~out out[0..7]=out2a, out[8..15]=out2b, out[15]=ng); // if (out<0) set ng = 1 !Or8Way(in=out2a, out=outa); Or8Way(in=out2b, out=outb); Or(a=outa, b=outb, out=nzr); !Not(in=nzr, out=zr); // if (out==0) set zr = 1

YUCK!Mux16(a=x, b=false, sel=zx, out=x2);

Mux16(a=y, b=false, sel=zy, out=y2); !Not16(in=x2, out=notx2); // if (zx==1) set x = 0 Not16(in=y2, out=noty2); // if (zy==1) set y = 0 !Mux16(a=x2, b=notx2, sel=nx, out=x3); // if (nx==1) set x = ~x Mux16(a=y2, b=noty2, sel=ny, out=y3); // if (ny==1) set y = ~y !Add16(a=x3, b=y3, out=add16); // if (f==1) set out = x + y And16(a=x3, b=y3, out=and16); // if (f==0) set out = x & y Mux16(a=and16, b=add16, sel=f, out=out1); !Not16(in=out1, out=notout); Mux16(a=out1, b=notout, sel=no, out=out, // if (no==1) set out = ~out out[0..7]=out2a, out[8..15]=out2b, out[15]=ng); // if (out<0) set ng = 1 !Or8Way(in=out2a, out=outa); Or8Way(in=out2b, out=outb); Or(a=outa, b=outb, out=nzr); !Not(in=nzr, out=zr); // if (out==0) set zr = 1

My Mind,

She Asplodes!

Mux16(a=y2, b=noty2, sel=ny, out=y3); // if (ny==1) set y = ~y !Add16(a=x3, b=y3, out=add16); // if (f==1) set out = x + y And16(a=x3, b=y3, out=and16); // if (f==0) set out = x & y Mux16(a=and16, b=add16, sel=f, out=out1); !Not16(in=out1, out=notout); Mux16(a=out1, b=notout, sel=no, out=out, // if (no==1) set out = ~out out[0..7]=out2a, out[8..15]=out2b, out[15]=ng); // if (out<0) set ng = 1 !Or8Way(in=out2a, out=outa); Or8Way(in=out2b, out=outb); Or(a=outa, b=outb, out=nzr); !Not(in=nzr, out=zr); // if (out==0) set zr = 1152

My Mind,

She Asplodes!

mux mux

mux muxNOT

NOT AND

mux mux

mux muxNOT

NOT AND

mux mux

mux muxNOT

NOT AND

Always

mux mux

mux muxNOT

NOT AND

Always

mux mux

mux muxNOT

NOT AND

Always

Both Multiple &

Partial!!

f(x,y)

zx zynx ny f no

mux mux

mux muxNOT

NOT AND

6 little flags = Instruction set

01 -1x y

!x !y-x -y

x+1 y+1x-1 y-1x+yx-y y-xx&y x|y

ALU in 440 NAND Gates By Mark Armbrust w/ Koen Simmons’ optimizations.

via forums for nand2tetris

Sequential Logic

Combinational vs

Sequential158

SomeLogicin out

Combinational Chips

InputLogic

OutputLogicMemoryin out

Sequential Chips

InputLogic

Sequential Chips

160Clock Input

DFF “Magic” Logic:

out(t) = in(t-1)

Atomic in nand2tetris

Can be created with nands!

Building a DFF using the TECS Hardware Simulator, by Mark Armbrust.

http://www.marksmath.com/tecs/dff/

From NAND to DFF

Details166

Interesting

in out

bitbit(t) = if load then in else bit(t-1) end !return bit(t)

in out

dff(t) = if load then in else dff(t-1) end !return dff(t)

in outdff

dff(t) = if load then in else dff(t-1) end !return dff(t)

inout mux dff

register

in out

in outbit0 bit1 bit15…

register

in0 out0

bit1in1 out1

bit2in2 out2

…inN outN

bit15in15 out15

Simple Linear Layout

register

in out

register

in out

register

in out

register

in out

InputLogic

Sequential Logic

register

in out

register

in out

register

in out

register

in out

…Addressing Addressing

InputLogic

register

in out

register

in out

register

in out

register

in out

…dmux8way mux8way

DFFBit

RegisterRam8Ram64Ram512Ram4KRam16K

DFFBit

RegisterRam8Ram64Ram512Ram4KRam16K

1bit×16

RAM64+?179

Again180

Exercise for the

“Reader”181

outcounter

resetincr

AKA Program Counter

Addresses current instruction

in ROM184

RegisterInc16

reset load inc

outMux16AND

RegisterInc16

reset load inc

outMux16AND

Blah Blah Logic

RegisterInc16

reset load inc

outMux16AND

The Magic

Blah Blah Logic

Memory

CPUInput

Output

Registers

Control

writeM

addressM

instruction

CPU Guts

address outROM32K

rom32k

outKeyboard

keyboard

screen

load outScreen8K words

address

keyboard

Screen

Keyboard

screen

Memory

CPUInput

Output

Registers

Control

computer

address outROM32K

writeM

addressM

instruction

keyboard

Screen

Keyboard

screen

Let’s Go Home!

apollo guidance computer197

Julian Simioni, MWRC 2014Software Development Lessons from the

Apollo Program

16-bit words.

Most software in ROM

Never had an error in flight.

http://www.ibiblio.org/apollo/ to fly your own.

2,800 dual 3-input

NOR ICs!!199

http://upload.wikimedia.org/wikipedia/commons/1/13/Agc_flatp.jpg

Thank You200

let's build a computer - zenspider.comryan/presentations/2014_gogaruco_lets_build… ·...

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