Seeing red

[The Grand Nudger]

Roger, simple gates only, just as a reference.  

As I said, at this point I can't understand how additional gates inside essentially a black box chip with defined inputs and outputs that match an exhaustive truth table, and do not store internal states (as is the case with these early chips), could offer additional control (what you refer to as utility rather than elegance) over the machine, but I'll take your word on it that it will all become clear in the next chapter  

As a black box chip absolutely irrelevant, correct. The shape of your black box is a hack box, is all. I was geeking out about boxes of different shapes.  There's a section dealing with that as well, little further on down. ALU's are my favorite part. Have fun.

[emjay]

Roger, simple gates only, just as a reference.  

As I said, at this point I can't understand how additional gates inside essentially a black box chip with defined inputs and outputs that match an exhaustive truth table, and do not store internal states (as is the case with these early chips), could offer additional control (what you refer to as utility rather than elegance) over the machine, but I'll take your word on it that it will all become clear in the next chapter  

As a black box chip absolutely irrelevant, correct. The shape of your black box is a hack box, is all. I was geeking out about boxes of different shapes.  There's a section dealing with that as well, little further on down.  ALU's are my favorite part.  Have fun.

Phew... I thought I was going insane there   Yes, I'll be interested to see what these hacks are all about, but when it comes up in the book   I think ALU's will be one of my favourite parts as well... I loved binary arithmetic at college... I love anything procedural. Would you like me to check in after every chapter and let you know my progress, or would you rather I just got on with it? It's just nice to get some feedback from the master  And rest assured I take everything you say on board, just as always 

btw, what software do you use to produce your schems? I don't think the software suite here comes with any software for that.

[The Grand Nudger]

You're looking for either an EDA or a schematic editor that;s compatible with your hdl file format.  Try TinyCad or KiCAD.  I use Eagle, but only out of habit and because I have the full suite.  EasyEDA runs in a browser tab......if that's your thing.  Pretty much all of the editors are cross platform.  

Just for what you want, KiCad (and it's user created libraries) is probably the way to go.  It has -alot- more functionality than just making symbol map schematics, though.

[emjay]

You're looking for either an EDA or a schematic editor that;s compatible with your hdl file format.  Try TinyCad or KiCAD.  I use Eagle, but only out of habit and because I have the full suite.  EasyEDA runs in a browser tab......if that's your thing.  Pretty much all of the editors are cross platform.  

Just for what you want, KiCad (and it's user created libraries) is probably the way to go.  It has -alot- more functionality than just making symbol map schematics, though.

Thanks for that, Rhythm, but unfortunately they all look a bit too complicated for me. I was just hoping for simple diagrams of the top level chips used in a HDL definition of a single chip... just showing pins and their connections, coming out of boxes with the chip name on... just something simple like that. Whereas these programs are very intricate, very technical, and they deal with the electronics which I'm guessing I'm not going to learn about in this course? In other words this course is abstract regarding the physical implementation of the chips on real circuitboards? But thanks for those suggestions... maybe in the future   At the moment I'll just make do with pen and paper

Anyway, I've now done chapter two and its project, so if you're interested, this is my implementation of the specified ALU:

---

Code:

// This file is part of www.nand2tetris.org
// and the book "The Elements of Computing Systems"
// by Nisan and Schocken, MIT Press.
// File name: projects/02/ALU.hdl

/**
* The ALU (Arithmetic Logic Unit).
* Computes one of the following functions:
* x+y, x-y, y-x, 0, 1, -1, x, y, -x, -y, !x, !y,
* x+1, y+1, x-1, y-1, x&y, x|y on two 16-bit inputs,
* according to 6 input bits denoted zx,nx,zy,ny,f,no.
* In addition, the ALU computes two 1-bit outputs:
* if the ALU output == 0, zr is set to 1; otherwise zr is set to 0;
* if the ALU output < 0, ng is set to 1; otherwise ng is set to 0.
*/

// Implementation: the ALU logic manipulates the x and y inputs
// and operates on the resulting values, as follows:
// if (zx == 1) set x = 0        // 16-bit constant
// if (nx == 1) set x = !x       // bitwise not
// if (zy == 1) set y = 0        // 16-bit constant
// if (ny == 1) set y = !y       // bitwise not
// if (f == 1)  set out = x + y  // integer 2's complement addition
// if (f == 0)  set out = x & y  // bitwise and
// if (no == 1) set out = !out   // bitwise not
// if (out == 0) set zr = 1
// if (out < 0) set ng = 1

CHIP ALU {
    IN  
        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 (if 1) or x & y (if 0)
        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

    PARTS:
   // Put you code here:
   Mux16(a=x,b=false,sel=zx,out=toamuxnx);
  
   Not16(in=toamuxnx,out=tobmuxnx);
   Mux16(a=toamuxnx,b=tobmuxnx,sel=nx,out=toxf);
  
   Mux16(a=y,b=false,sel=zy,out=toamuxny);
  
   Not16(in=toamuxny,out=tobmuxny);
   Mux16(a=toamuxny,b=tobmuxny,sel=ny,out=toyf);
  
   And16(a=toxf,b=toyf,out=toamuxf);
   Add16(a=toxf,b=toyf,out=tobmuxf);
   Mux16(a=toamuxf,b=tobmuxf,sel=f,out=toamuxno);
  
   Not16(in=toamuxno,out=tobmuxno);
   Mux16(a=toamuxno,b=tobmuxno,sel=no,out=out,out[0..7]=outor8w1,out[8..15]=outor8w2,out[15..15]=ng);
  
   Or8Way(in=outor8w1,out=outora);
   Or8Way(in=outor8w2,out=outorb);
   Or(a=outora,b=outorb,out=outtonot);
   Not(in=outtonot,out=zr);
}

---

What I'm liking about this particularly is that it's developing a whole new way of thinking... a whole new type of logic. In the sense that in traditional programming if you have branching statements... as in if... do this, else... do something else ...you can consider one or another branch a dead end. But here it's different... here there are no switches per se diverting the path of inputs based on flags (ie the control bits) - which tbh is what I assumed was happening before - rather everything is done in parallel... you can't just stop an output dead once you're finished with it, it has to go somewhere... so for instance in this ALU you have a control bit to negate the input, but to implement it you have to do (or I had to do) both whatever the case... so take the input and negate it down one path, and then feed both the both the negated and the non-negated paths into a Mux which outputs one or the other depending on the value of the control bit. So it's a very different type of logic than I'm used to but I'm really enjoying learning it  

On with the next chapter, Sequential Logic, and from the looks of it, that will be the one about making memories  

[The Grand Nudger]

They're made for building boards, yeah, they go beyond the projects you're doing. They can also be used to make those schematics I've been linking in this thread, though. I'm glad you're enjoying it.

[emjay]

They're made for building boards, yeah, they go beyond the projects you're doing.  They can also be used to make those schematics I've been linking in this thread, though.  I'm glad you're enjoying it.

It does look cool, don't get me wrong, just over my head at the moment. Maybe one day

I've done chapter three now... flip-flops, registers, RAM, and a program counter. It's really good because I'm learning how these things really work - it's demystifying it no end I spent forever on the program counter though... all day I understood what it needed to do and how it worked but I had trouble working out how to model an if, else-if, else-if, else with muxes. I think I'm starting to understand that now though... put the top-most if closest to the register... then the second top-most back from that and so on. And also I forgot that the register should be loading all the time in this case, just from different sources, so I wasted a lot of time trying to debug when I was setting the load bit of the register to the load control bit, but in the end just changed it to the constant true. But anyway, I think it's probably about time I stopped giving you updates on my progress because they're well and truly off-topic for this thread and stopping it die a natural death. But I'll let you know when I've finished and thanks again for introducing me to it, and for all the wonderful discussion we've had in this thread over the last month or so

[The Grand Nudger]

Hehehe, yeah, it's a tangent, let's bring it back round and in, shall we?  Demystifying those circuits, demystifies our experience.  It may not explain it, but understanding how those systems work can explain how "stuff" -can- produce the effects we attribute to mind, even if we do it Some Other Way™, even if, ultimately, it's other stuff or different principles in action, in our case.

We might not be able to say "this is how we see red" - but we can describe how a computer sees red..and exhaustively so, all the way down to the quirks of a program counter's mechanical implementation.

Consider, for example, the way your circuits simply accept an input as true. That's required, mechanically, to do logic - a quirk just like the placement of mux in-circuit. It might seem puzzling that a logic machine can produce illogical statements, conclusions...but they clearly can..if and when that true input is standing in as the variable for whether or not a truth statement X -exists-, is stored in memory. The system takes it to be true, it does logic, and all is for naught at the end because it produces a gibberish statement such as "All birds are made of iron" -is true-.

We have a similar habit, in that we often assess the truth value of a claim by what we have stored in memory, regardless of the truth value of the statement in relation to some exterior or even objective standard. We might have seen a 6 inch crappie, and, when asked "is this a big crappie" we're answering, essentially, whether or not that crappie is bigger than the crappie of memory - our answer may not be representative of the size of crappie as a species, but it -will- be representative of those statements regarding crappie and size taken as true by us, based upon those inputs we are confined by in assessing anything.

A comparator can answer that question just as easily as we can, and it will succeed or fail in answering those questions by varying standards for precisely the same reasons and in precisely the same scenarios. In both cases the following occurs, if the crappie is larger than the crappie of memory, the conclusion is true, yes...that's a big crappie. If it's smaller, the reverse. If the crappie of memory is particularly large, then our statement "no, that is not a big crappie" is true referent only to the system.....outside of that the crappie in question might be very large indeed. If our crappie of memory is very small.....again the reverse. Why?

[emjay]

Hehehe, yeah, it's a tangent, let's bring it back round and in, shall we?  Demystifying those circuits, demystifies our experience.  It may not explain it, but understanding how those systems work can explain how "stuff" -can- produce the effects we attribute to mind, even if we do it Some Other Way™, even if, ultimately, it's other stuff or different principles in action, in our case.

We might not be able to say "this is how we see red" - but we can describe how a computer sees red..and exhaustively so, all the way down to the quirks of a program counter's mechanical implementation.

Consider, for example, the way your circuits simply accept an input as true.  That's required, mechanically, to do logic - a quirk just like the placement of mux in-circuit.  It might seem puzzling that a logic machine can produce illogical statements, conclusions...but they clearly can..if and when that true input is standing in as the variable for whether or not a truth statement X -exists-, is stored in memory.  The system takes it to be true, it does logic, and all is for naught at the end because it produces a gibberish statement such as "All birds are made of iron" -is true-.

We have a similar habit, in that we often assess the truth value of a claim by what we have stored in memory, regardless of the truth value of the statement in relation to some exterior or even objective standard.  We might have seen a 6 inch crappie, and, when asked "is this a big crappie" we're answering, essentially, whether or not that crappie is bigger than the crappie of memory - our answer may not be representative of the size of crappie as a species, but it -will- be representative of those statements regarding crappie and size taken as true by us, based upon those inputs we are confined by in assessing anything.  

A comparator can answer that question just as easily as we can, and it will succeed or fail in answering those questions by varying standards for precisely the same reasons and in precisely the same scenarios.  In both cases the following occurs, if the crappie is larger than the crappie of memory, the conclusion is true, yes...that's a big crappie.  If it's smaller, the reverse.  If the crappie of memory is particularly large, then our statement "no, that is not a big crappie" is true referent only to the system.....outside of that the crappie in question might be very large indeed.  If our crappie of memory is very small.....again the reverse.  Why?

Interesting example   I think I have very different views on 'truth' than most people on here so whenever there's a 'what is truth?' type thread I don't get involved because I don't take it for granted that what we 'believe' is true. To me, the feeling - if that's what it is - of believing something is not a measurement of truth but of the activation of a mental representation. In childhood 'make-believe', hypnosis, and dreams there is activation of mental representations but they don't necessarily correspond to reality, but nonetheless they have a feeling of belief... as in a feeling of being real. Likewise I think if a neurosurgeon came along and directly stimulated the binding neuron(s) of a particular context, at whatever level of abstraction, it would translate to the feeling of that mental representation being true/real. Basically because a neuron is a detector and it's activation measures the degree of 'truth' that whatever it has learned to detect is 'out there'. If it's firing hard it means very true/certain, but if it's just over threshold... on but firing at the minimum level... then that would represent something more like 'possible', '50-50', or 'maybe'.

To put what I'm saying into context, any time you identify something in life you follow the same process. In order to identify something you have to already have a representation of it in your mind. And in this sense a representation is just a binding neuron... a means of associating a group of features into one unit... in other words a means of categorising something by its features. You notice one feature of something. If it's enough to trigger the binding neuron... just get it into the 'maybe' level of activation then bidirectional feedback will start biasing the other associated features, making them easier to activate. Activate the next feature... the binding neuron activation goes higher, feedbacks more, biases more. And also, as this feedback comes down, it not only biases some neurons but it actually takes others above threshold and activates them. These neurons that come on during the settling process are what I believe are assumptions... things you take as true without necessarily being aware of them or where they came from If you've ever played any hidden object games they're very enlightening as to how bias and assumptions can really impede your ability to find whatever it is you're looking for. Anyway, there you go; rapid identification of an object due to bidirectional feedback and the bootstrapping effect.

If on the other hand there is no representation of something in your mind... ie it's a novel object/place etc... you've got to wait until a neuron takes up the job of associating its features before you can start having expectations about it (where 'expectation' is represented by the bidirectional biasing feedback). Which will happen, over time, given enough repeated presentations of the novel environment/object/place etc. Each pass of learning will extract as it were the stable features of that environment/object/idea etc and associate them. The learning process is complicated but in case it means anything to you, or is of any interest to you, it's Hebbian model learning, and the way Emergent models it is with an algorithm called CPCA - Conditional Principal Components Analysis.

The point is that you identify something by the presence of its features, and the level of 'truth' is a measure of how activated the detector of those features is. But the same process works at any level of abstraction... so identifying objects and lower right up to abstract ideas and beyond. And IMO, high activation of such contexts - indicating the presence of activated features corresponds to the feeling of truth/belief/real. But, and this is a big but, I'm not talking about individual binding neurons so much as entire contexts... ie related sets of associations... self-sustained feedback loops of bidirectional activation. This is how I see it: I think there is a limit to how many contexts can be active in your mind at once (I call it your 'mindscape') and I think it's the magic number 7+ or -2 as I learned about in psychology. That is to say, how many completely unrelated things you can remember (ie if they were related they'd be part of the same context). I don't know if you had 'The Generation Game' over there with Bruce Forsyth but in it was the prize conveyor belt where various prizes scrolled by - TV's, picnic hampers, champagne etc - and any that the contestant could remember they got to keep. But they never could remember all of them because they're not contextually related. Anyway I believe that context limitation is effected by the level of inhibition in the binding layers which is to say that only a certain number of binding neurons can be on in the layers at any given time.

So I think the feeling of belief is a measure of the activation of a whole context that's in mental focus. The biggest context that's active in the mind is the present... all the sensory data of the present. So from this state that you always return to, what does it take to activate another mental context to the extent that you believe it is real? That is to say, how do you literally make-believe? Real life is the stronger context... you are bombarded with 'truth' from your senses... and while active it will contradict anything you try to imagine as being real. So in other words if I try to imagine eating an apple so much so that I believe I am eating an apple, my reality context is stopping that from happening by essentially saying 'wtf are you talking about?, you're not eating an apple and here's the sensory data from your taste buds to prove it' So whilst the reality context is impeding, it's stopping the intended context from activating... stopping it from being believed. But if you were not aware of reality, there would be nothing to contradict it, and it could become activated, including with a corresponding sense of real/truth/belief, and with full bidirectional feedback to speed it along on it's way to becoming fully active. This is what I believe hypnosis is. Since you have a limited mindscape, in the sense that only so many things can be in focus at the same time, the more you focus inward, the more it pushes out your sense awareness, until it's no longer constraining your imaginary context which then feels real. At that point you're fully lost in a make-believe world, daydream, hypnosis, or even just a good book... until you snap out of it for whatever reason, back into the real world and the reality context again. And of course in dreaming you're completely cut off from constraining sensory data but yet you still believe whatever you're presented with as true... in a dream world you can believe 'all birds are made of iron'

So there's me just gone off on probably a tangent as usual How to relate this to what you're saying about crappies We assess the truth of something referent to our own memories... yep I get that... because our memories are in fact the detectors of them in the first place (ie they're mental representations) But there are certain things that could be considered fairly objective standards in the sense that our neurons, at least at the sensory level, model the statistical regularities of the environment... lines, colours,gravity etc. So they're objective in the sense that there are certain things to model that everyone will experience the same regardless of where they are... it's only when thoughts and ideas become more abstract and when you're considering episodic memory more than model learning that the referents become more idiosyncratic and internal and lead to different appraisals of the relative sizes of crappies

[bennyboy]

About 7 +/- 2, I don't think it's about "contexts." I'm pretty sure it's how many separate entities or bits of information your mind can track at one time. And then, there's chunking, which I guess you mean by context, though I don't think you mentioned learning as the binding force of a given context. Maybe I'm not understanding you, and for sure I forget a lot from my psych courses 20 years ago.

As for your biggest context being the present, that I'm not sure about. I think the idea of self is the biggest context, and then the world view. That's why things like self-generation of ideas lead to better recall, perhaps: it connects say a new word you're learning in a language to the narrative of the self.

Just being argumentative here. You said SO many things that were right on and interesting, but those are the thigns I arbitrarily picked to engage on.

[emjay]

About 7 +/- 2, I don't think it's about "contexts."  I'm pretty sure it's how many separate entities or bits of information your mind can track at one time.  And then, there's chunking, which I guess you mean by context, though I don't think you mentioned learning as the binding force of a given context.  Maybe I'm not understanding you, and for sure I forget a lot from my psych courses 20 years ago.

As for your biggest context being the present, that I'm not sure about.  I think the idea of self is the biggest context, and then the world view.  That's why things like self-generation of ideas lead to better recall, perhaps: it connects say a new word you're learning in a language to the narrative of the self.

Just being argumentative here.  You said SO many things that were right on and interesting, but those are the thigns I arbitrarily picked to engage on.

I never learnt about 7 +/- 2 in the context of contexts either But in my understanding of contexts since then, I started to see the two could be related, but it's just a theory. My psych courses were about 15 years ago and I've forgotten all about chunking. But yes I have mentioned that learning is the binding force of contexts (in fact it's my mantra )... associative learning... that's what contexts are... collections of self-sustaining and related associations. So not just a tree of associations but a tree that relies on a tree that relies on a tree that feeds back into the first one etc and therefore can maintain activation just by network dynamics even when it's no longer receiving input.

No, I'm not sure about that either, especially after this thread where I've come to a new understanding of the self. So I'll give you that one... the biggest context could be the present in the sense of sensory awareness or it could be the self, or both, with self as one more object but that's a bit confusing... so I think for my own sanity I'll keep talking and thinking in the first person

Thank you And no problem... let the arguments... discussions... commence I've missed you