Tag Archives: full-adder

Final States

Over the last three posts I’ve been exploring the idea of system states and how they might connect with computational theories of mind. I’ve used a full-adder logic circuit as a simple stand-in for the brain — the analog flow and logical gating characteristics of the two are very similar.

In particular I’ve explored the idea that the output state of the system doesn’t reflect its inner working, especially with regard to intermediate states of the system as it generates the desired output (and that output can fluctuate until it “settles” to a valid correct value).

Here I plan to wrap up and summarize the system states exploration.

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Intermediate States

I left off last time talking about intermediate, or transitory, states of a system. The question is, if we only look at the system at certain key points that we think matter, do any intermediate states make a difference?

In a standard digital computer, the answer is a definite no. Even in many kinds of analog computers, transitory states exist for the same reason they do in digital computers (signals flowing through different paths and arriving at the key points at different times). In both cases they are ignored. Only the stable final state matters.

So in the brain, what are the key points? What states matter?

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State of the System

State DiagramIn the last post I talked about software models for a full-adder logic circuit. I broke them into two broad categories: models of an abstraction, and models of a physical instance. Because the post was long, I was able to mention the code implementations only in passing (but there are links).

I want to talk a little more about those two categories, especially the latter, and in particular an implementation that bridges between the categories. It’s here that ideas about simulating the brain or mind become important. Most approaches involve some kind of simulation.

One type of simulation involves the states of a system.

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Full-Adder “Computing”

Full Adder Logic TableImagine the watershed for a river. Every drop of water that falls in that area, if it doesn’t evaporate or sink into the ground, eventually makes its way, through creeks, streams, and rivers, to the lake or ocean that is the shed’s final destination. The visual image is somewhat like the veins in a leaf. Or the branches of the leaf’s tree.

In all cases, there is a natural flow through channels sculpted over time by physical forces. Water always flows downhill, and it erodes what it flows past, so gravity, time, and the resistance of rock and dirt, sculpt the watershed.

The question is whether the water “computes.”

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Sideband #61: Tock

relaysYou’ve been waiting for the other shoe to drop, right? The tick to finally tock? (My clock is — as usual — running a bit behind; this should be #62, but that’s another story.) Today’s tale involves electro-mechanical logic! Computing with relays rather than solid-state gates.

Rather than the tick-tock of a mechanical clock, the tock-tick of lots and lots of relays! Aisle after aisle of racks of relays, many thousands of them all clicking away like chattering insects. That’s what is (or was) inside some of those windowless buildings found in every neighborhood with local phone service.

However, today the focus is quite a bit smaller…

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Logically Speaking

ttab adder fullIf it hasn’t been apparent, I’ve been giving a bit of a fall semester in some computer science basics. If it seems complicated, well, the truth is all we’ve done is peek in some windows. From a safe distance. And most of the blinds were down.

I thought we’d finish (yes, finish!) with a bang and take a deep dive down into the lowest levels of a computer, both on the engineering side and on the abstract logic side. When they say, “It’s all ones and zeros,” these are the bits (in both senses!) they mean.

Attention: You need to be at least this geeky for this ride!

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