diff --git a/main.py b/main.py
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+++ b/main.py
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+import numpy as np # helps with the math
+import matplotlib.pyplot as plt # to plot error during training
+
+# input data
+inputs = np.array([[0, 0, 1, 0],
+                   [0, 0, 1, 1],
+                   [0, 0, 0, 0],
+                   [1, 1, 0, 0],
+                   [1, 1, 1, 1],
+                   [1, 1, 0, 1]])
+# output data
+outputs = np.array([[0], [0], [0], [1], [1], [1]])
+
+# create NeuralNetwork class
+class NeuralNetwork:
+
+    # intialize variables in class
+    def __init__(self, inputs, outputs):
+        self.inputs  = inputs
+        self.outputs = outputs
+        # initialize weights as .50 for simplicity
+        self.weights = np.array([[.50], [.50], [.50], [0.50]])
+        self.error_history = []
+        self.epoch_list = []
+
+    #activation function ==> S(x) = 1/1+e^(-x)
+    def sigmoid(self, x, deriv=False):
+        if deriv == True:
+            return x * (1 - x)
+        return 1 / (1 + np.exp(-x))
+
+    # data will flow through the neural network.
+    def feed_forward(self):
+        self.hidden = self.sigmoid(np.dot(self.inputs, self.weights))
+
+    # going backwards through the network to update weights
+    def backpropagation(self):
+        self.error  = self.outputs - self.hidden
+        delta = self.error * self.sigmoid(self.hidden, deriv=True)
+        self.weights += np.dot(self.inputs.T, delta)
+
+    # train the neural net for 25,000 iterations
+    def train(self, epochs=25000):
+        for epoch in range(epochs):
+            # flow forward and produce an output
+            self.feed_forward()
+            # go back though the network to make corrections based on the output
+            self.backpropagation()    
+            # keep track of the error history over each epoch
+            self.error_history.append(np.average(np.abs(self.error)))
+            self.epoch_list.append(epoch)
+
+    # function to predict output on new and unseen input data                               
+    def predict(self, new_input):
+        prediction = self.sigmoid(np.dot(new_input, self.weights))
+        return prediction
+
+# create neural network   
+NN = NeuralNetwork(inputs, outputs)
+# train neural network
+NN.train()
+
+# create two new examples to predict                                   
+example = np.array([[1, 1, 1, 0]])
+example_2 = np.array([[0, 0, 1, 1]])
+
+# print the predictions for both examples                                   
+print(NN.predict(example), ' - Correct: ', example[0][0])
+print(NN.predict(example_2), ' - Correct: ', example_2[0][0])
+
+# plot the error over the entire training duration
+plt.figure(figsize=(15,5))
+plt.plot(NN.epoch_list, NN.error_history)
+plt.xlabel('Epoch')
+plt.ylabel('Error')
+plt.savefig('plot.png')
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