Boolean Funcitons

Artificial Neuron will have X for input and y for output, the output y from all of x value multiply the weight and plus the bias with bias weight.

  • $x$: x value, $w$: weight,

    $$ y = \sum_{i=1}^N (x_i * w_i) + (bias)(bias_{weight}) $$



OR

x1 x2 y
0 0 0
0 1 1
1 0 1
1 1 1 
1
2
3
4
5
6
7
8
9
10
11
12
class create_OR:

    def forward(self, X):
        x1 = X[0]
        x2 = X[1]
        x1_WEIGHT = 1
        x2_WEIGHT = 1
        CONSTANCE = 1
        CONSTANCE_WEIGHT = 0
        result = x1 * x1_WEIGHT + x2 * x2_WEIGHT + CONSTANCE * CONSTANCE_WEIGHT

        return {True: 1, False: 0} [result > 0]

AND

x1 x2 y
0 0 0
0 1 0
1 0 0
1 1 1 
1
2
3
4
5
6
7
8
9
10
11
12
class create_AND:
    
    def forward(self, X):
        x1 = X[0]
        x2 = X[1]
        x1_WEIGHT = 1
        x2_WEIGHT = 1
        CONSTANCE = 1
        CONSTANCE_WEIGHT = -1
        result = x1 * x1_WEIGHT + x2 * x2_WEIGHT + CONSTANCE * CONSTANCE_WEIGHT

        return {True: 1, False: 0} [result > 0]

NOT

x y
0 1
1 0 
1
2
3
4
5
6
class create_NOT:

    def forward(self, X):
        result = X

        return {True: 1, False: 0} [result == 0]

XNOR

x1 x2 y
0 0 1
0 1 0
1 0 0
1 1 1 
1
2
3
4
5
6
7
8
9
10
11
class create_XNOR:

    def forward(self, X):
        x1 = X[0]
        x2 = X[1]

        xAND = create_AND().forward([x1, x2])
        xNotAND = create_AND().forward([create_NOT().forward(x1), create_NOT().forward(x2)])
        xOR = create_OR().forward([xAND, xNotAND])

        return xOR

XOR

x1 x2 y
0 0 0
0 1 1
1 0 1
1 1 0 
1
2
3
4
5
6
7
class create_XOR:

    def forward(self, X):
        XNOR = create_XNOR().forward(X)
        XOR = create_NOT().forward(XNOR)
        
        return XOR
2019-04-14