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How would I go about converting this Boolean expression so that it would only use NAND gates in its circuit?

A ⋅ ¬B ⋅ ¬D + ¬A ⋅ B ⋅ ¬C ⋅ D

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  • \$\begingroup\$ Take deMorgan's on it. \$\endgroup\$ – StainlessSteelRat Dec 9 '18 at 22:17
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If your expression was: \$f = ¬A ⋅ ¬B ⋅ C ⋅ D + A ⋅ B ⋅ ¬C\$

$$¬A ⋅ ¬B ⋅ C ⋅ D + A ⋅ B ⋅ ¬C$$ deMorgans: Invert expression, change + to ⋅ and invert terms.

$$\overline {\overline {¬A ⋅ ¬B ⋅ C ⋅ D} ⋅ \overline {A ⋅ B ⋅ ¬C}}$$

All NANDs.

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Ok, so you have to apply deMorgan's theorem in order to have only NAND gates. I don't want to solve your expresion but I can give you an example: enter image description here will be enter image description here that will be enter image description here

So you have to invert the expressions and change + (OR) with * (AND) .

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