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Numerical problems Continued
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Q7. For the given network, calculate the net input to the output neuron.

enter image description here

Solution: $y_{in}=0.5\times 1+0.2\times 0.5+0.3\times 0.9+(-0.6)\times 0.2+(-0.1)\times 0.3$

$y_{in}=0.5+0.10+0.18-0.12-0.03$

$y_{in}=0.18$

Q8. Calculate the output of neuron $Y$ for the net shown in figure. Use binary and bipolar sigmoidal activation functions. ![enter image description here][2] \lt/div\gt Solution: The net input: $y_{in}=b+x_1w_1+x_2w_2$ $y_{in}=0.9+0.2\times 0.7+0.3\times 0.8$ $y_{in}=0.9+0.14+0.24$ $y_{in}=1.28$ (i) Binary Sigmoidal Activation Function $y=f(y_{in})=\dfrac 1{1+e^{-y_{in}}}=\dfrac 1{1+e^{-1.28}}$ (ii) Bipolar Sigmoidal Activation Function, $y=f(y_{in})=\dfrac 2{1+e^{-y_{in}}}-1=\dfrac {1-e^{-1.28}}{1+e^{-1.28}}$ \lt/div\gt \ltDIV class='paper-question'\gt \ltDIV class='paper-ques-desc'\gt \ltb\gtQ9.\lt/b\gt Design neutral using M-P neuron to implement using binary input (i) NOT logic (ii) OR (iii) NAND \lt/div\gt Solution: (i) OR ![enter image description here][3] $y_{in}=x_1w_1+x_2w_2$ Case 1: Assume $w_1=w_2=1$ $(1,1) - y_{in}=2$ $(1,0) - y_{in}=1$ $(0,1) - y_{in}=1$ $(0,0) - y_{in}=0$ Setting threshold as 2 will not work. Case 2: Assume $w_1=1, w_2=-1$ $(1,1) - y_{in}=0$ $(1,0) - y_{in}=1$ $(0,1) - y_{in}=-1$ $(0,0) - y_{in}=0$ Setting threshold as 1 will not work. Case 3: Assume $w_1=-1, w_2=1$ $(1,1) - y_{in}=0$ $(1,0) - y_{in}=-1$ $(0,1) - y_{in}=1$ $(0,0) - y_{in}=0$ Setting threshold as 1 will not work. Case 4: Assume $w_1=-1, w_2=-1$ $(1,1) - y_{in}=-2$ $(1,0) - y_{in}=-1$ $(0,1) - y_{in}=-1$ $(0,0) - y_{in}=0$ $\theta\ge nw-p\\theta\ge2\times(0)-1\\theta\ge-1$

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