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logicsubtractioncircuit

Full subtractor using half adders

Is it possible to create a full subtractor using half adders only? I have created a circuit with 2 half adders but cannot see how I can use half adders to get the borrow.

This is what I have done so far: https://i.sstatic.net/sO6bK.png

I need to know if this can be done using half adders only.

Solution

  • Implementation using half subtractors only:

    (a) We use the borrow out of a half subtractor to create a HS that has the same function of an AND gate.

    (b) We can also use a HS with the first input = 1 to get the complementary output (the same function of a NOT gate.

    We put (b) after (a)'s output and we have a NAND gate. Everything can be implemented using NAND or NOR gates. So here's the final circuit:

    https://i.sstatic.net/cpPhN.png

    We have created the equivalents of AND, OR gates using our new NAND "gates".