I have created my truth table and drawn from this a boolean expression (f = B'A' + CA' + DC' + DB + D'CB') which I have then attempted to convert into a circuit using Quartus.
I am new to digital logic and I need some help from someone wit experience who can tell me if what I have attempted looks correct.
I am unable to compile the circuit as I don't have 'device support installed'. If anyone could point me in the right direction for how to obtain that, that would be greatly appreciated.
This is the circuit I created based on the boolean expression.
This is my truth table. The circuit corresponds to the f column
Everything to the left of your AND gates looks mathematically correct (although not very efficient). You can drastically reduce the amount of NOT gates used.
Instead of splitting the signals before the NOT gates and having each individual branch have its own NOT gate, you can split the signals after the NOT gate thus reducing the total amount of NOT gates used.
Anyway, the fundamental reason your circuit is invalid is because of the very right part of it, here:
You are shorting together the outputs of two gates, which is not allowed. A single node cannot simultaneously have two separate voltages.
What you need to do to fix this problem is take each individual output of your 5 AND gates and take them all to a separate input of a 5-input OR gate.
Something like this:
If this software package that you are using doesn't support five inputs to a gate, then you can split it up like so:
Related
I'm reading the Digital Design and Computer Architecture by David Harris, Sarah Harris. The authors give the following definition of combinational logic:
A combinational circuit’s outputs depend only on the current values of
the inputs; in other words, it combines the current input values to
compute the output... A combinational circuit is memoryless, but a
sequential circuit has memory. The functional specification of a
combinational circuit expresses the output values in terms of the
current input values.
However, they claim this circuit is not combinational:
because "node n6 connects to the output terminals of both I3 and I4". Indeed, it's one of the designated signs when a scheme can not be combinational but, according to the authors:
Certain circuits that disobey these rules are still combinational, so
long as the outputs depend only on the current values of the inputs.
As I'm able to catch on, the aforementioned circuit is the case: its output is 1 if and only if its inputs are both 1, otherwise the output is 0. So the output is defined as a function of the inputs (the AND function).
In fact, there was already a question about this circuit in the computer science network and it has an accepted answer. Here's an excerpt from it:
Circuit (d) cannot be written in this form [of formula], since the
outputs of I3 and I4 are wired together. What is the relation between
the input to the rightmost gate and the outputs of I3 and I4? Not
something that can be described combinatorially.
Unfortunately, I'm still confused due to
The circuit, regarded as a black box, is still in scope of the combinational logic definition: its output values depend only on the current values of the inputs;
The relation between the input to the rightmost gate and the outputs of I3 and I4 can be described through the function NAND of the circuit inputs and this function is quite "memoryless". It's not obvious for me why we can't afford to depict a gate input using multiple outputs of other gates.
I need some elaboration. Maybe things would fall into place if someone provide a circuit example when two gates outputs is connected to one input and it actually causes "memory" (in contrast to the considered sample).
Circuit (d) is not combinational because it is not a logic gate circuit at all.
I think it's a very silly example to explain combinational vs sequential circuits.
In a logic circuit, an output wire cannot go to another output wire. You assumed that the outputs, when connected together, will act as a logical OR or AND of themselves.
This is not true (otherwise why would we use AND/OR gates in the first place?).
What will happen depends on the specific implementation of the gates (i.e. specific IC or manufacturing process you used) and this is not something that a logic circuit is meant to model.
A logic circuit must behave the same, no matter what brand you are using.
In circuit (d), the output of I3 will feed both the input of the rightmost NOT and the output of I4 (the complementary is also true).
Most IC will break if a current will flow in from their outputs, others won't but they will interfere with the capability of the right-most NOT to sense its input.
Logic circuits are still circuits, so you should, in theory, perform a full circuit analysis, which includes solving differential equations, to solve for their output.
Digital electronics is a branch that abstracts from these "low-level" details but at the cost of making some assumptions, one of which is: outputs are never merged without a gate.
The whole point of a combinational circuit is that you can write out = f(in0, in1, ..., ink) but it's not always possible.
Take for example an edge detector, it is just a f(A) = (NOT A) AND A which should, by the law of the excluded middle, always output 0.
But it will not because the NOT A path takes a slightly longer time to reach the AND input.
How can you describe this dynamic behaviour with a f(A) function?
Don't think too much of it, when you'll get to sequential circuits you'll spot the difference immediately (if you need a preview, look up for "latch circuit").
It is very confusing while googling for LSTM gates , I find that some references and articles say that they are three gates: input , forget and output gates , While others say that they are four gates : learn , forget , remember, and use gate ?
So, what is the right ?
There are four gates: input modulation gate, input gate, forget gate and output gate, representing four sets of parameters.
We can see that there are four sets of parameters(8 matrices) colored in blue in the below graph of LSTM where f stands for the forget gate, g and i the add gate, o the output gate. Since the add gate needs two sets of parameters we can combine them as just one gate.
Reference:
Speech and Language Processing
Long Short Term Memory networks – usually just called “LSTMs” – are a special kind of RNN, capable of learning long-term dependencies. So there are different types of LSTMs, LSTMs have chain-like structure like RNN, but the repeating module has a different structure. Instead of having a single neural network layer, there are four, interacting in a very special way. However, there are many variants of LSTMS.
Ref: http://colah.github.io/posts/2015-08-Understanding-LSTMs/
I'm making a simple electric circuit simulator. It will (at least initially) only feature batteries, wires and resistors in series and parallel. However, I'm at a loss how best to simulate said circuit in a good way.
Specifically, I will have batteries and resistors with two contact points each, and wires that go between two contact points. I assume that each component will have a field for its resistance, the current through it and the voltage across it (current and voltage will, of course, be signed). Each component is given a resistance, and the batteries are given a voltage. The goal of the simulation is to assign correct values to all the other fields in real time as the player connects and disconnects components and wires.
These are the requirements:
It must be correct, including Ohm's and Kirchhoff's laws (I'm modeling real world circuits, and there is little point if the model does something completely different)
It must be numerically stable (we can't have uncontrolled oscillations or something just because two neighbouring resistors can't make up their minds together)
It should stabilize relatively quickly for, let's say, fewer than 30 components (having to wait a few seconds before the values are correct doesn't really satisfy "real time", but I really don't plan on using it for more than 10 or maybe 20 components)
The optimal formulation for me (how I envision this in my head) would be if I could assign a script to each component that took care of that component only, possibly by communicating field values with neighbouring components, and each component script works in parallel and adjusts as is needed
I only see problems here and no solutions. The biggest problem, I think, is Kirchhoff's voltage law (going around any sub-circuit, the voltage across all components, including signs, add up to 0), because that's a global law (it says somehting about a whole circuit and not just a single component / connection point). There is a mathematical reformulation saying that there exists a potential function on the points in the circuit (for instance, the voltage measured against the + pole of the battery), which is a bit more local, but I still don't see how to let a component know how much the voltage / potential drops across it.
Kirchhoff's current law (the net current flow into an intersection is 0) might also be trouble. It seems to force me to make intersections into separate objects to enforce it. I originally thought that I could just let each component have two lists (a left list and a right list) containing every other component that is connected to it at that point, but that might not make KCL easily enforcable.
I know there are circuit simulators out there, and they must have solved this exact problem somehow. I just can't find an explanation because if I try googling it, I only find the already made simulators and no explanations anywhere.
I have a rather large(not too large but possibly 50+) set of conditions that must be placed on a set of data(or rather the data should be manipulated to fit the conditions).
For example, Suppose I have the a sequence of binary numbers of length n,
if n = 5 then a element in the data might be {0,1,1,0,0} or {0,0,0,1,1}, etc...
BUT there might be a set of conditions such as
x_3 + x_4 = 2
sum(x_even) <= 2
x_2*x_3 = x_4 mod 2
etc...
Because the conditions are quite complex in that they come from experiment(although they can be written down in logic form) and are hard to diagnose I would like instead to use a large sample set of valid data. i.e., Data I know satisfies the conditions and is a pretty large set. i.e., it is easier to collect the data then it is to deduce the conditions that the data must abide by.
Having said that, basically what I'm doing is very similar to neural networks. The difference is, I would like an actual algorithm, in some sense optimal, in some form of code that I can run instead of the network.
It might not be clear what I'm actually trying to do. What I have is a set of data in some raw format that is unique and unambiguous but not appropriate for my needs(in a sense the amount of data is too large).
I need to map the data into another set that actually is ambiguous to some degree but also has certain specific set of constraints that all the data follows(certain things just cannot happen while others are preferred).
The unique constraints and preferences are hard to figure out. That is, the mapping from the non-ambiguous set to the ambiguous set is hard to describe(which is why it is ambiguous). The goal, actually, is to have an unambiguous map by supplying the right constraints if at all possible.
So, on the vein of my initial example, I'm given(or supply) a set of elements and need some way to derive a list of constraints similar to what I've listed.
In a sense, I simply have a set of valid data and train it very similar to neural networks.
Then, after this "Training" I'm given the mapping function I can then use on any element in my dataset and it will produce a new element satisfying the constraint's, or if it can't, will give as close as possible an unambiguous result.
The main difference between neural networks and what I'm trying to achieve is I'd like to be able to use have an algorithm to code to be used instead of having to run a neural network. The difference here is the algorithm would probably be a lot less complex, not need potential retraining, and a lot faster.
Here is a simple example.
Suppose my "training set" are the binary sequences and mappings
01000 => 10000
00001 => 00010
01010 => 10100
00111 => 01110
then from the "Magical Algorithm Finder"(tm) I would get a mapping out like
f(x) = x rol 1 (rol = rotate left)
or whatever way one would want to express it.
Then I could simply apply f(x) to any other element, such as x = 011100 and could apply f to generate a hopefully unambiguous output.
Of course there are many such functions that will work on this example but the goal is to supply enough of the dataset to narrow it down to hopefully a few functions that make the most sense(at the very least will always map the training set correctly).
In my specific case I could easily convert my problem into mapping the set of binary digits of length m to the set of base B digits of length n. The constraints prevents some numbers from having an inverse. e.g., the mapping is injective but not surjective.
My algorithm could be a simple collection if statements acting on the digits if need be.
I think what you are looking for here is an application of Learning Classifier Systems, LCS -wiki. There are actually quite a few LCS open-source applications available, but you may need to experiment with the parameters in order to get a good result.
LCS/XCS/ZCS have the features that you are looking for including individual rules that could be heavily optimized, pressure to reduce the rule-set, and of course a human-readable/understandable set of rules. (Unlike a neural-net)
I have several datasets i.e. matrices that have a 2 columns, one with a matlab date number and a second one with a double value. Here an example set of one of them
>> S20_EavesN0x2DEAir(1:20,:)
ans =
1.0e+05 *
7.345016409722222 0.000189375000000
7.345016618055555 0.000181875000000
7.345016833333333 0.000177500000000
7.345017041666667 0.000172500000000
7.345017256944445 0.000168750000000
7.345017465277778 0.000166875000000
7.345017680555555 0.000164375000000
7.345017888888889 0.000162500000000
7.345018104166667 0.000161250000000
7.345018312500001 0.000160625000000
7.345018527777778 0.000158750000000
7.345018736111110 0.000160000000000
7.345018951388888 0.000159375000000
7.345019159722222 0.000159375000000
7.345019375000000 0.000160625000000
7.345019583333333 0.000161875000000
7.345019798611111 0.000162500000000
7.345020006944444 0.000161875000000
7.345020222222222 0.000160625000000
7.345020430555556 0.000160000000000
Now that I have those different sensor values, I need to get them together into a matrix, so that I could perform clustering, neural net and so on, the only problem is, that the sensor data was taken with slightly different timings or timestamps and there is nothing I can do about that from a data collection point of view.
My first thought was interpolation to make one sensor data set fit another one, but that seems like a messy approach and I was thinking maybe I am missing something, a toolbox or function that would enable me to do this quicker without me fiddling around. To even complicate things more, the number of sensors grew over time, therefore I am looking at different start dates as well.
Someone a good idea on how to go about this? Thanks
I think your first thought about interpolation was the correct one, at least if you plan to use NNs. Another option would be to use approaches which are designed to deal with missing data, like http://en.wikipedia.org/wiki/Dempster%E2%80%93Shafer_theory for example.
It's hard to give an answer for the clustering part, because I have no idea what you're looking for in the data.
For the neural network, beside interpolating there are at least two other methods that come to mind:
training separate networks for each matrix
feeding them all together to the same network, with a flag specifying which matrix the data is coming from, i.e. something like: input (timestamp, flag_m1, flag_m2, ..., flag_mN) => target (value) where the flag_m* columns are mutually exclusive boolean values - i.e. flag_mK is 1 iff the line comes from matrix K, 0 otherwise.
These are the only things I can safely say with the amount of information you provided.