<p>The <a href="https://en.wikipedia.org/wiki/multigrade_operator" class="extiw" title="w:multigrade operator">multigrade operation</a> <i>all <a href="https://en.wikipedia.org/wiki/exclusive_or" class="extiw" title="w:exclusive or">or</a> nothing</i> of the arguments in the parentheses to the left of the matrix
</p><p>Red squares stand for binary ones, respectively for <i><a href="https://en.wikipedia.org/wiki/truth_value" class="extiw" title="w:truth value">true</a></i>. 130 of 256 squares are red.
</p><p>This operation is <i><a href="https://en.wikipedia.org/wiki/Logical_conjunction" class="extiw" title="w:Logical conjunction">AND</a> <small><a href="https://en.wikipedia.org/wiki/Exclusive_or" class="extiw" title="w:Exclusive or">XOR</a></small> <a href="https://en.wikipedia.org/wiki/Logical_NOR" class="extiw" title="w:Logical NOR">NOR</a></i>  :
</p><p><span style="white-space:nowrap"><a href="//commons.wikimedia.org/wiki/File:Multigrade_operator_AND.svg" class="image"><img alt="Multigrade operator AND.svg" src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/74/Multigrade_operator_AND.svg/150px-Multigrade_operator_AND.svg.png" decoding="async" width="150" height="121" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/7/74/Multigrade_operator_AND.svg/225px-Multigrade_operator_AND.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/7/74/Multigrade_operator_AND.svg/300px-Multigrade_operator_AND.svg.png 2x" data-file-width="361" data-file-height="291"></a>   <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ~\oplus ~}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mtext> </mtext><mo>⊕<!-- ⊕ --></mo><mtext> </mtext></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle ~\oplus ~}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c767eb37cbb7ba0cb1dd95c05efe9daf890806a2" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.505ex; width:4.002ex; height:2.176ex;" alt="{\displaystyle ~\oplus ~}"></span>   <a href="//commons.wikimedia.org/wiki/File:Multigrade_operator_NOR.svg" class="image"><img alt="Multigrade operator NOR.svg" src="https://upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Multigrade_operator_NOR.svg/150px-Multigrade_operator_NOR.svg.png" decoding="async" width="150" height="121" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Multigrade_operator_NOR.svg/225px-Multigrade_operator_NOR.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Multigrade_operator_NOR.svg/300px-Multigrade_operator_NOR.svg.png 2x" data-file-width="361" data-file-height="291"></a>       <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ~\Leftrightarrow ~}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mtext> </mtext><mo stretchy="false">⇔<!-- ⇔ --></mo><mtext> </mtext></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle ~\Leftrightarrow ~}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2bb31f1ac4db02ffdbeb50c9369b8c78eec14d7" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:4.775ex; height:1.843ex;" alt="{\displaystyle ~\Leftrightarrow ~}"></span>       <a href="//commons.wikimedia.org/wiki/File:Multigrade_operator_all_xor_nothing.svg" class="image"><img alt="Multigrade operator all xor nothing.svg" src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/75/Multigrade_operator_all_xor_nothing.svg/150px-Multigrade_operator_all_xor_nothing.svg.png" decoding="async" width="150" height="121" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/7/75/Multigrade_operator_all_xor_nothing.svg/225px-Multigrade_operator_all_xor_nothing.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/7/75/Multigrade_operator_all_xor_nothing.svg/300px-Multigrade_operator_all_xor_nothing.svg.png 2x" data-file-width="361" data-file-height="291"></a></span>
</p><p>Apart from the line with no arguments it's the same as <i><a href="https://en.wikipedia.org/wiki/Logical_conjunction" class="extiw" title="w:Logical conjunction">AND</a> <small><a href="https://en.wikipedia.org/wiki/Logical_disjunction" class="extiw" title="w:Logical disjunction">OR</a></small> <a href="https://en.wikipedia.org/wiki/Logical_NOR" class="extiw" title="w:Logical NOR">NOR</a></i>  :
</p>
<span style="white-space:nowrap"><a href="//commons.wikimedia.org/wiki/File:Multigrade_operator_AND.svg" class="image"><img alt="Multigrade operator AND.svg" src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/74/Multigrade_operator_AND.svg/150px-Multigrade_operator_AND.svg.png" decoding="async" width="150" height="121" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/7/74/Multigrade_operator_AND.svg/225px-Multigrade_operator_AND.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/7/74/Multigrade_operator_AND.svg/300px-Multigrade_operator_AND.svg.png 2x" data-file-width="361" data-file-height="291"></a>   <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ~\lor ~}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mtext> </mtext><mo>∨<!-- ∨ --></mo><mtext> </mtext></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle ~\lor ~}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/155cea7ee0773ed86f00911071974ee73e80e269" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:3.744ex; height:2.009ex;" alt="{\displaystyle ~\lor ~}"></span>   <a href="//commons.wikimedia.org/wiki/File:Multigrade_operator_NOR.svg" class="image"><img alt="Multigrade operator NOR.svg" src="https://upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Multigrade_operator_NOR.svg/150px-Multigrade_operator_NOR.svg.png" decoding="async" width="150" height="121" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Multigrade_operator_NOR.svg/225px-Multigrade_operator_NOR.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Multigrade_operator_NOR.svg/300px-Multigrade_operator_NOR.svg.png 2x" data-file-width="361" data-file-height="291"></a>       <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ~\Leftrightarrow ~}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mtext> </mtext><mo stretchy="false">⇔<!-- ⇔ --></mo><mtext> </mtext></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle ~\Leftrightarrow ~}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2bb31f1ac4db02ffdbeb50c9369b8c78eec14d7" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:4.775ex; height:1.843ex;" alt="{\displaystyle ~\Leftrightarrow ~}"></span>       <a href="//commons.wikimedia.org/wiki/File:Multigrade_operator_all_or_nothing.svg" class="image"><img alt="Multigrade operator all or nothing.svg" src="https://upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Multigrade_operator_all_or_nothing.svg/150px-Multigrade_operator_all_or_nothing.svg.png" decoding="async" width="150" height="121" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Multigrade_operator_all_or_nothing.svg/225px-Multigrade_operator_all_or_nothing.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Multigrade_operator_all_or_nothing.svg/300px-Multigrade_operator_all_or_nothing.svg.png 2x" data-file-width="361" data-file-height="291"></a></span>
<table><tbody><tr><td style="padding: 15px;"><a href="//commons.wikimedia.org/wiki/File:Watchduck.svg" class="image"><img alt="Watchduck.svg" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Watchduck.svg/40px-Watchduck.svg.png" decoding="async" width="40" height="46" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Watchduck.svg/60px-Watchduck.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Watchduck.svg/80px-Watchduck.svg.png 2x" data-file-width="703" data-file-height="806"></a>
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<td><a href="//commons.wikimedia.org/wiki/User:Watchduck" title="User:Watchduck">Watchduck</a><br><span style="color: gray; font-size: 80%;">You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".</span>
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<span class="int-own-work" lang="en">Own work</span>