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Q.	what are the characteristic of a combinational logic circuits in a digital system?	Related Search: Other - Electronics
	how to design, construct & test combinational logic circuits using only basic gates?
A.	The main characteristic of combinational logic is that there are no flip-flops. That is, there is no storage or memory of past events. There is no 'clock' there are only inputs and outputs. When you apply different inputs to a combo. logic circuit, the output changes immediately (with normal propagation delays). Whenever you change the inputs, the outputs change. .

Q.	Would a state machine in 3 dimensions be the same as combinational logic in 4 dimensions?	Related Search: Physics
	Suppose you take a state machine(a machine who's output is dependant on its inputs and the internal state of the machine) and take the dimension of time and turn it into a 4th spacial dimension, would we then have a 4 dimensional combinational machine(a machine whos outputs are only dependant on its inputs)? I've always pondered wether time could be viewed as a fourth spacial dimension, if there was anything unique about time that made it different from the other spacial dimensions. Wether we, as humans just percieve it differently.
A.	What a strange question... I would say NO! and here is why: A state machine is a purely mathematical concept that uses neither the notion of space or time, therefor it is independent of any physical implementation. And even if you went at the problem from a thermodynamic/information theoretical perspective for physical implementations of state machines, naively I would have to say that because a state machine stores information while combinatorial logic does not, the entropy associated with the two systems would have to be different. I said naively... which means I am waiting to be proven wrong by someone who has done the math rather than giving a hand waveing argument. Now... I suppose there is a second interpretation of your question, which stays completely in the realm of abstract math, which is probably: "Can one unfold a state machine into a purely combinatorial representation?" And the answer to that would be, yes, one can. One way you do it is by removing the internal state and by making it a second set of inputs. This is equivalent to formulating the s sub n+1 = f sub SM(s sub n, x sub n) feedback as a recursive function s sub n+1 = f sub SM(y sub s, x sub n), where y sub n is f sub SM(y sub n-1, x sub n-1) etc. and ultimately y sub 0 becomes the initial state s sub initial. So at any given moment, the output of the state machine is a mapping from the s sub initial state and all external states x sub i=0..n which happened between the initial state and the current state. For a non-trivial state machine this recursive function can be enormously complex! In practice the computational complexity to calculate that function is most likely an NP complete problem, although, for special machines like counters etc., you can pre-compute the output easily. Advanced digital simulators/design provers do these things on the fly to save time (let's say you need to simulate a 32 bit counter... would you make 2^32 steps through the simulator or rather just use the clock cycle counter to represent the output at any given time?). Hope this gives some food for thought.

Q.	What are the ways of detecting and eliminating combinational logic hazrds?	Related Search: Other - Education
	You can tell me directly what are these hazrds or you can send me a site where I can find the answers. Thank you.
A.	Start with Wiki: [Link] > [Link] This is a fascinating subject, and you've reminded me that it's been on my "to do" list for some time. Thanks! I've been engaged in a long-running dispute with a fundamentalist Christian about some of the arguments used to bolster "creation science" (what an oxymoron that is!) and have been meaning to check for more ammo. So I'm going to take my own advice and go read those articles right now! [BTW, for those Christian flamers out there chomping at the bit to condemn me to the fire, I have no particular problem with your belief system. BUT it is NOT science and should not be presented in public school science classrooms supported by tax dollars. Take your arguments to the debating society or philosophy class.]

Q.	whats the difference between a combinational logic device and the seqentual logic device?	Related Search: Mathematics
	i need to know the difference in how it operates, what it does, just the difference between them, someone please help.
A.	combinational logic just is a collection of gates like AND and OR that have an output state that is determined by the input state. In sequential logic the output state depends on the input and also some previous history.

Q.	Compare the operation of a combinational logic device and a sequential logic device?	Related Search: Mathematics
	Explain the operational difference of the two and the advantages of one over the other. Give a working example of each. thanks :) im not, it's a criteria i have to complete for college. To be honest, i shouldn't have to do this subject, but its so that i get more points overall.
A.	OK In a combinational logic device, the output changes a short time after the input changes. The delay depends on the time it takes the signal to get through the device. In a sequential device, the output changes a short time after the clock input changes, and at no other time. The delay therefore depends generally on the clock speed and not on the delay through the device. An example of a combinational logic device is a NAND gate. An example of a sequential logic device is a flip-flop. A digital system generally consists of a number of flip-flops, the input of each being fed from a network of combinational devices. The inputs of these combinational devices may come from outside the system, or they may come from the outputs of flip-flops. This is known as a "synchronous" system as its state changes on the clock edge. A design consisting only of combinational devices is known as an "asynchronous" system, as its state changes whenever the inputs change. The key advantage of an asynchronous system is speed - you get the answer in the fastest possible time. However, you may get problems with "race" conditions, in which the answer may vary according to which signals travel fastest through the system and which input to a device arrives first. A synchronous system avoids this problem (usually) by allowing all signal propagations to settle before updating the state of the system but, of course, it will always be slower than an asynchronous system.

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Not to be confused with combinatory logic, a topic in mathematical logic.

In digital circuit theory, combinational logic (sometimes also referred to as combinatorial logic) is a type of digital logic which is implemented by boolean circuits, where the output is a pure function of the present input only. This is in contrast to sequential logic, in which the output depends not only on the present input but also on the history of the input. In other words, sequential logic has memory while combinational logic does not.

Combinational logic is used in computer circuits to do Boolean algebra on input signals and on stored data. Practical computer circuits normally contain a mixture of combinational and sequential logic. For example, the part of an arithmetic logic unit, or ALU, that does mathematical calculations is constructed using combinational logic. Other circuits used in computers, such as half adders, full adders, half subtractors, full subtractors, multiplexers, demultiplexers, encoders and decoders are also made by using combinational logic.

1 Representation
2 Logic formulas minimization
3 See also
4 References

[edit] Representation

Combinational logic is used for building circuits where certain outputs are desired, given certain inputs. The construction of combinational logic is generally done using one of two methods: a sum of products, or a product of sums. A sum of products can be easily visualized by looking at a truth table:

$A$	$B$	$C$	Result	Logical equivalent
F	F	F	F	$\neg A \cdot \neg B \cdot \neg C$
F	F	T	F	$\neg A \cdot \neg B \cdot C$
F	T	F	F	$\neg A \cdot B \cdot \neg C$
F	T	T	F	$\neg A \cdot B \cdot C$
T	F	F	T	$A \cdot \neg B \cdot \neg C$
T	F	T	F	$A \cdot \neg B \cdot C$
T	T	F	F	$A \cdot B \cdot \neg C$
T	T	T	T	$A \cdot B \cdot C$

Using sum of products, we take the sum of all logical statements which yield true results. Thus, our result would be:

$A \cdot \neg B \cdot \neg C + A \cdot B \cdot C \,$

It could then be simplified using Boolean algebra to:

$A \cdot (\neg B \cdot \neg C + B \cdot C) \,$

[edit] Logic formulas minimization

Minimization (simplification) of combinational logic formulas is produced on the basis of the following rules:

$(A + B) \cdot (A + C) = A + (B \cdot C), \quad (A \cdot B) + (A \cdot C) = A \cdot (B + C);$

$A + (A \cdot B) = A, \quad A \cdot (A + B) = A;$

$A + (\lnot A \cdot B) = A + B,\quad A \cdot(\lnot A + B) = A \cdot B;$

$(A + B)\cdot(\lnot A + B)=B, \quad (A \cdot B) + (\lnot A \cdot B)=B.$

$(A \cdot B) + (\lnot A \cdot B) + (B \cdot C) = (A \cdot B) + (\lnot A \cdot B);$

Owing to minimization logical function is simplified, and combinational circuit becomes more compact and convenient for realization.

[edit] See also

[edit] References

Combinational Logic & Systems Tutorial Guide by D. Belton, R. Bigwood.

Retrieved from "http://en.wikipedia.org/wiki/Combinational_logic"

Categories: Discrete mathematics | Mathematical logic

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