Electrical – How to represent a SOP in terms of NAND

digital-logiclogic-gates

Is there a specific technique to convert SOPs to NAND.

I have the following expression:

A'BC + ABC'

And would like to represent it using only NAND gates.

A'BC=(((AB')')'C')'

ABC'=(((A'B')')'C')'

But now, how can you represent the or part using NAND gate?

Best Answer

Do following procedure:

Step 1: Convert all NOT-operators

Step 2: Convert all AND-operators (left to right)

Step 3: Convert all OR-operators (left to right)

How to do it?:

Convert NOT-operator: X¯=X⊕X

Convert AND-operator: X⋅Y=(X⊕Y)⊕(X⊕Y)

Convert OR-operator: X+Y=(X⊕X)⊕(Y⊕Y)

Related Solutions

Electronic – Is it possible to implement SOP with 4 terms by only 3 NAND gates

It makes sense, because if you look at the function, there are pairs of terms in which C appears both negated and not; so it has no influence on the output; and, if you look at the truth table, the same applies.

$$ {\lnot C} + {C} = 1 $$ and $$ AB \cdot (C+ \lnot C)=AB \cdot 1 = AB $$

So you can just discard C.

Showing three functions with Decoder 3-8

If you connected them:

A -> i-0
B -> i-1
C -> i-2

It looks good to me.

Note that:

F3 = F1 + A'BC

So F3's OR gate only needs to be 2-inputs, at the cost of latency.

Best Answer

Related Solutions

Electronic – Is it possible to implement SOP with 4 terms by only 3 NAND gates

Showing three functions with Decoder 3-8

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