<p>For 3 inputs it's not <span class="math-container">$2^3$</span> functions but <span class="math-container">$2^{2^3}$</span> functions. Circuit minimization is generally hard. You could try using the aiger package <a href="http://fmv.jku.at/aiger/" rel="nofollow noreferrer">http://fmv.jku.at/aiger/</a>, which will give you a circuit but not necessarily minimal.</p>

CC BY-SA 4.0
2019-11-08T17:20:11.800Z
2019-11-08T17:20:11.800Z
Mikolas
<p>I need to know for each of the <span class="math-container">$2^{2^3}$</span> boolean functions with <span class="math-container">$3$</span> inputs the
smallest boolean circuit made only of NAND gates computing it (smallest in terms
of the number gates). </p>

<p>I would be glad if someone could tell me a source where I can look this up
or a clever procedure to find the minimal circuits myself. </p>

<boolean-functions><circuits><minimization>
How to find for each 3-input boolean function the minimum number of NAND operators needed to compute it
dnn
# How to find for each 3-input boolean function the minimum number of NAND operators needed to compute it

(Asked by: username_0 on 2019-11-08)

I need to know for each of the $2^{2^3}$ boolean functions with $3$ inputs the
smallest boolean circuit made only of NAND gates computing it (smallest in terms
of the number gates).

I would be glad if someone could tell me a source where I can look this up
or a clever procedure to find the minimal circuits myself.

**Tags:** boolean-functions, circuits, minimization


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## 1 answers

### Answer by username_1 on 2019-11-08. Score: 1

For 3 inputs it's not $2^3$ functions but $2^{2^3}$ functions. Circuit minimization is generally hard. You could try using the aiger package <http://fmv.jku.at/aiger/>, which will give you a circuit but not necessarily minimal.


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