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Miloslav Ciz 2024-12-13 20:40:56 +01:00
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logic_gate.md
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@ -58,7 +58,7 @@ The truth table of these gates is as follows:
*symbols often used for logic gates*
Functions NAND and NOR are [functionally complete](functional_completeness.md) which means we can implement any other gate with only one of these gates. For example NOT(x) = NAND(x,x), AND(x,y) = NAND(NAND(x,y),NAND(x,y)), OR(x,y) = NAND(NAND(x,x),NAND(y,y)) etc. Similarly NOT(x) = NOR(x,x), OR(x,y) = NOR(NOR(x,y),NOR(x,y)) etc. NAND and NOR are the only two functions that are functionally complete by themselves, but there are more functionally complete sets of multiple functions, for example OR together with NOT can also implement any other function (which can be seen from the fact that we can implement NOR as NOT(OR(x,y), and we know NOR is already functionally complete). More detail on this will follow below.
Functions NAND and NOR are [functionally complete](functional_completeness.md) which means we can implement any other gate with only one of these gates. For example NOT(x) = NAND(x,x), AND(x,y) = NAND(NAND(x,y),NAND(x,y)), OR(x,y) = NAND(NAND(x,x),NAND(y,y)) etc. Similarly NOT(x) = NOR(x,x), OR(x,y) = NOR(NOR(x,y),NOR(x,y)) etc. NAND and NOR are the only two functions that are functionally complete by themselves, but there are more functionally complete sets of multiple functions, for example OR together with NOT can also implement any other function (which can be seen from the fact that we can implement NOR as NOT(OR(x,y)), and we know NOR is already functionally complete). More detail on this will follow below.
## More Detail On Boolean Functions