I have a system built only NAND implementing this function.

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I have to process this function using only De Morgan's law and finally get only negation conjuction functions.

I did it but I'm not sure is it good. Could you help me?

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++++ UPDATE: I did this gate also in CEDAR, is it correct? enter image description here


1 Answer 1


$$Y = (X_1 \cdot X_2) + \overline {(X_3 \cdot \overline {X_1}) + X_2} $$

Double negation: \$ X = \overline{\overline{X}}\$

$$Y = \overline {\overline {(X_1 \cdot X_2) + \overline {(X_3 \cdot \overline {X_1}) + X_2}}} $$

Take deMorgan's:

$$Y = \overline {\overline {(X_1 \cdot X_2)} \cdot \overline {\overline {(X_3 \cdot \overline {X_1}) + X_2}}} $$

Take deMorgan's on 2nd term:

$$Y = \overline {\overline {(X_1 \cdot X_2)} \cdot \overline {\overline {(X_3 \cdot \overline {X_1})} \cdot \overline {X_2}}} $$

  • \$\begingroup\$ Thank you for help. Now I know where I did a mistake. \$\endgroup\$
    – Lauro Mike
    Apr 15, 2020 at 21:51

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