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mathlogiccircuit

Write logic gates from logic gate circuit

Could someone please show me how to write the logic from this logic circuit?

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Following you guys' explanation, I have these results, am I right:

enter image description here

The question is which one of a, b, c, d produces the same ouput as the first circuit. I don't see any similar results here, please illuminate me !

Solution

  • If you give names to the intermediate terms, e.g. S and T, where S is the output of the AND gate and T is the output of the inverter (NOT gate), then you can break it down as follows:

    X = S | T                ; final OR gate
S = A & B                ; output of AND gate
T = ~B                   ; output of inverter (NOT gate)
X = (A & B) | ~B         ; substitute above

    Note that this is a poor example as the expression can be reduced to:

    X = ~(~A & B)

    which can be implemented with just two gates (a NAND and a NOT), or

    X = A | ~B

    which can also be implemented with two gates (an OR and a NOT).