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Miloslav Ciz 2023-11-13 16:29:28 +01:00
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logic_circuit.md
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@ -23,7 +23,7 @@ Generally a logic circuit can be seen as a "black box" that has *N* input bits a
Logic circuits can be drawn simply as "boxes" (which one the base level are the basic logic gates such as [AND](and.md), [OR](or.md) etc.) connected with lines ("wires", but again not really electronic wires as here only 1 or 0 can be carried by such wire). But as mentioned, their behavior can also be described with a truth table (which however says nothing about the internals of the circuit) or a boolean expression, i.e. an algebraic expression that for each of the circuit outputs defines how it is computed from the outputs, for example *a = !x & y* and *b = !(y | z)* for the above drawn example circuit. Each of these types of representation has its potential advantages -- for example the graphical representation is a very human-friendly representation while the algebraic specification allows for optimization of the circuits using algebraic methods. Many hardware design languages therefore allow to use and combine different methods of describing logic circuits (some even offer more options such as describing the circuit behavior in a programming language such as [C](c.md)).
With combinational logic circuits it is possible to implement any boolean function (i.e. "functions only with values 1 and 0"); [undecidability](undecidability.md) doesn't apply here as we're not dealing with [Turing machines](turing_machine.md) computations because the output always has a finite, fixed number of bits, the computation can't end up in an infinite loop as there are no repeating steps, just a straightforward propagation of input values to the output. It is always possible to implement any function at least as a [look up table](lut.md) (which can be created with a [multiplexer](multiplexer.md)). Sequential logic circuits on the other hand can be used to make the traditional computers that work in steps and can therefore get stuck in loop and so on.
With combinational logic circuits it is possible to implement any boolean function (i.e. "functions only with values 1 and 0"); [undecidability](undecidability.md) doesn't apply here as we're not dealing with [Turing machines](turing_machine.md) computations because the input and output always has a finite, fixed number of bits, the computation can't end up in an infinite loop as there are no repeating steps, just a straightforward propagation of input values to the output. It is always possible to implement any function at least as a [look up table](lut.md) (which can be created with a [multiplexer](multiplexer.md)). Sequential logic circuits on the other hand can be used to make the traditional computers that work in steps and can therefore get stuck in loop and so on.
Once we've designed a logic circuit, we can [optimize](optimization.md) it which usually means making it use fewer logic gates, i.e. make it cheaper to manufacture (but optimization can also aim for other things, e.g. shortening the maximum length from input to output, i.e. minimizing the circuit's [delay](delay.md)).