Summary / Instructions

I was given this problem in a test paper:

Take this circuit enter image description here

and make an equivalent one only with NAND gates.

The problem

I've tried, with multiple combinations but almost always the result is in this form:

Where it's supposed to be in this form X*X+X, the function of the above circuit.

NOT A AND NOT B AND C , ~A*~B + C (~ = NOT, * = AND, + = OR)


I know I'm not supposed to just throw the problem ( like asking others to get it solve ) but I'm feeling frustrated and I have a final exam soon and I know this kind of question will be in, any help is greatly appreciated.

  • 4
    \$\begingroup\$ De Morgan's laws might be useful. \$\endgroup\$ – Andy aka May 23 '17 at 12:03
  • \$\begingroup\$ The logic function is ~(A*B)+C, or ~A+~B+C. \$\endgroup\$ – JimmyB May 23 '17 at 13:02

An OR gate can be made with only NAND gate (the most common gate btw) thanks to DeMorgan's theorem.


simulate this circuit – Schematic created using CircuitLab

You can find on this website some more simplification in the world of boolean algebra.

  • 1
    \$\begingroup\$ Normally I'd criticise an answer that just handed over an homework/exam answer rather than gave guidance. But I can't see any way of answering it in smaller steps, it's a DeMorgan's question, so good answer. \$\endgroup\$ – TonyM May 23 '17 at 12:31

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