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Logic Circuit

Logic circuits are circuits made of logic gates that implement Boolean functions, i.e. they are "schematics to process 1s and 0s". They are used to design computers. Logic circuits are a bit similar to electronic circuits but are a level of abstraction higher: they don't work with continuous voltages but rather with discrete binary logic values: 1s and 0s. Logical circuits can be designed and simulated with specialized software and languages such as VHDL.

Generally a logic circuit has N input bits and M output bits. Then we divide logic circuits into two main categories:

With logic circuits it is possible to implement any boolean function; undecidability doesn't apply here as we're not dealing with Turing machines computations because the output always has a finite, fixed width, 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 (which can be created with a multiplexer).

Once we've designed a logic circuit, we can optimize 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). The optimization can be done with a number of techniques such as manual simplification of the circuit's logic expression or with Karnaugh maps.

Some common logic circuits include:



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