New Considerations for Spectral Classification of Boolean Switching  Functions

<table>Matrices representing (a) the starting function <svg height="14.75" id="M245" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 118.75 14.75" width="118.75" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.75)">
<g transform="translate(72,-60.2)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑓</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.01,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
<text transform="matrix(1,0,0,-1,-60.14,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">𝑋</tspan>
<tspan style="font-size: 12.50px; " x="14.040869" y="0">)</tspan>
<tspan style="font-size: 12.50px; " x="21.680202" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="33.708088" y="0">𝑥</tspan>
</text>
<text transform="matrix(1,0,0,-1,-19.54,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">3</tspan>
</text>
<text transform="matrix(1,0,0,-1,-11.89,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">+</tspan>
<tspan style="font-size: 12.50px; " x="11.340221" y="0">𝑥</tspan>
</text>
<text transform="matrix(1,0,0,-1,6.33,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
<text transform="matrix(1,0,0,-1,11.2,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑥</tspan>
</text>
<text transform="matrix(1,0,0,-1,18.08,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
</g>
</g>
</svg> and (b) the function <svg height="14.6" id="M246" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 37.650002 14.6" width="37.650002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑓</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.01,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
<text transform="matrix(1,0,0,-1,-60.14,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">𝑋</tspan>
<tspan style="font-size: 12.50px; " x="14.040869" y="0">)</tspan>
</text>
</g>
</g>
</svg> resulting from replacing each variable with the network <svg height="13.925" id="M247" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 84.400002 13.925" width="84.400002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.925)">
<g transform="translate(72,-60.86)">
<text transform="matrix(1,0,0,-1,-71.95,64.16)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑥</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.07,61.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">3</tspan>
</text>
<text transform="matrix(1,0,0,-1,-57.42,64.16)">
<tspan style="font-size: 12.50px; " x="0" y="0">⊕</tspan>
<tspan style="font-size: 12.50px; " x="13.303192" y="0">𝑥</tspan>
</text>
<text transform="matrix(1,0,0,-1,-37.24,61.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
<text transform="matrix(1,0,0,-1,-29.59,64.16)">
<tspan style="font-size: 12.50px; " x="0" y="0">⊕</tspan>
<tspan style="font-size: 12.50px; " x="13.303192" y="0">𝑥</tspan>
</text>
<text transform="matrix(1,0,0,-1,-9.4,61.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
</g>
</g>
</svg>.</table>

VLSI Design

fig3

Figure 3

Figure 3: New Considerations for Spectral Classification of Boolean Switching  Functions 