A question about ICA

[AltruismAndCake]

I figured I would ask this in the forums so everyone could get a chance to answer my question: Is ICA a form of CLE or RCA? I ask this question because of the parts of the adder... if the piston being up is propagate and the AND down below is the generate, doesn't that satisfy g0+p0g1+p0p1Cin?

The piston is attached to a xnor, but that's what we want for up to equal propagate.
I wanted to double check. Thank you for your time.

[greatgamer34]

ICA is in no form similar to CLE.... ICA is a form of RCA. Try building an ICA without pistons, it resembles an RCA. ICA uses one carry line, CLE uses multiple carry lines..

[TSO]

It is very much a ripple carry adder. A carry look ahead adder will actually have additional logic to compute the values of the carry before it arrives, (thus a look-ahead) while a ripple carry adder will have the vale of the carry pass through the adder of each individual digit before being allowed to move to the next digit. In general, ripple carry is slower; but in minecraft, the "instant" nature of restone (up to fifteen blocks, of course) makes it possible to create ripple carry adders that are faster than the equivalent carry look ahead adder.

[AltruismAndCake]

The design
i know i didn't finish the design but would this be an example of CLE, if it were finished?

[TSO]

...I have just discovered that redstone schematics are completely unreadable. From the picture, I have absolutely no idea.

Here, this is what I usually refer to.

What you are interested in is farther down the document, but I advise you still read the whole thing. Also, remember that some of the trade-offs described have no meaning to us (like fanout.)

If you have any questions about things in the source just ask me.

[AltruismAndCake]

OK I think I understand now but I want to double check. g0+p0g1+p0p1g2+p0p1p2Cin is NOT the formula for CLA or CLE. It only calculates Cout. You can build an RCA that uses that uses propagate and generate. It's the way you use propagate and generate that determines what kind of machine it is.

Also G[i:k] OR (P[i:k] AND G[k-1:j]) was a little confusing at first. I wasn't sure if it was one binary digit or multiple binary digits. Thank you for your time.

[TSO]

If we rotate some of your indicies, it forms the correct carry out. Cout will be P3P2P1P0Cin + P3P2P1G0 + P3P2G1 + P3G2 + G3

The double indices aren't extremely important, but in the blue box just above that, it defines P[i:i] to be Ai xor Bi and G[i:i] to be Ai * Bi.
With i representing the index of the first number and j being the index of the second number. Because they have the same weight, 2^(i), they already work together just fine. k represented the weight of the values being considered. So G[k-1:j] comes from the product (AND) of two numbers of weight 2^(k-1) while P[i:k] comes from the parity (XOR) of two numbers of weight 2^k. The other thing is that those wires in the box drawings all represent two trace wires one for P and one for G.

I'm surprised you didn't ask what the cube meant. Two of its dimensions are actually of some significance in minecraft.

[AltruismAndCake]

You mean the cube that shows what you trade off(more logic chips, more fanout, more wiring) for the speed your adder gets? You already told me that fanout is no problem in minecraft. Does that mean Sklansky's adder is the best CLA in minecraft?

[TSO]

Not what the cube means. The cube represents the physical dimension the circuit will grow in, the number assigned is the rate it grows at. An adder with more logic stages must be longer... because it has more logic stages. An adder with greater fanout must be wider because the traces need to be widened in order to lower their transfer resistance (and thus Beat Generation and dissipation). The ones with more wire crossings must be taller because wire crossing is done by vertically tracing into the next level up in order to jump over the wire(s) it must cross. Speed is basically in the L direction, power consumption is mostly in the f direction, and while the t direction also has a lot of effect on power, t mainly indicates the cost, complexity, and construction time of the design.

Fanout describes the maximum number of inputs that are attached to the output of one logic gate (how many gates share the same wire). If we were to randomly say that each gate consumes three Watts of power, your source gate must be able to maintain 3fW min without melting. This means for each gate you add into the fanout, you have to make this source and wire that much bigger. This is not a problem in Minecraft.

With that in mind, look at the Stalinsky adder, paying special attention to it's traces. Look at an insa-carry adder. Tell me what you see.

[greatgamer34]

Altruism learned from adzuck that ICA is different from RCA, this is why he is confused.

[AltruismAndCake]

What are you talking about? I never met adzuck before this post