Electrical – Circuit Using only NAND and NOT Gates

digital-logic

I have the following expressions for some logic which will each power a motor:

  1. A OR (NOT B) OR D
  2. NOT(A AND C) or (NOT C AND D)

I have a limitation on the number of integrated circuits I can use, with each IC being able to hold 6 of any 1 gate type on it.

I have tried below to turn both of the expressions below into circuits using only two types of gate, NOT and NAND gates, I know that I can create a NOT gate using a NAND gate with both of its inputs being into the NAND but I don't believe it makes too much of a difference for my requirements.

Circuit 1

schematic

simulate this circuit – Schematic created using CircuitLab

Circuit 2:

schematic

simulate this circuit

If possible, I want to be able to combine the circuits together, having 4 inputs A B C D with each of the outputs to the motor being separate I'm looking to keep the number of IC's as little as possible – 2 MAX.

Formatted the question since the first post made hardly any sense, Sorry!

Best Answer

You really cannot simplify \$A + \bar B + D\$.

But \$ \overline {A C} + \bar C D\$ can be simplified. Take deMorgan's on first term.

\$ \bar A + \bar C + \bar C D = \bar A + \bar C ( 1 + D ) = \bar A + \bar C = \overline {A C}\$

No possibility of combining the two circuits.

So using NANDs as NOTs, you have 6 NANDs total.

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