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Binary Step Function

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Binary step function is one of the most common activation function in neural networks out there. But before we get into it let's take a look at what activation functions and neural networks are.

Table of contents:

  1. Brief overview of neural networks and activation functions
  2. What is binary step function?
  3. Conclusion

Brief overview of neural networks and activation functions

Neural networks are a powerful machine learning mechanism that mimic how the human brain learns. Perceptrons are the basic building blocks of a neural network. A perceptron can be defined as anything that takes multiple inputs and produces one output.

Activation functions are mathematical equations that determine the output of a neural network. They basically decide to deactivate neurons or activate them to get the desired output thus the name, activation functions.
In a neural network, input data points are fed into the neuron. Each neuron has a respective weight which are multiplied by the inputs and added to a staic bias value(unique to each neuron).

x = (weight * input) + bias

This is then passed to an apropriate activation function.

Y = Activation function(โˆ‘(weight*input) + bias)

The output achieved will be again fed into the neurons in the next layer and the same process is repeated.

Activation functions can be categorized into three main categories:

  • Binary Step Function
  • Linear Activation Function
  • Non-Linear Activation functions
    • Sigmoid function
    • tanh function
    • ReLU function

to name a few.

What is binary step function?

Binary step function is one of the simplest activation functions. The function produces binary output and thus the name binary step funtion. The function produces 1 (or true) when input passes a threshold limit whereas it produces 0 (or false) when input does not pass threshold.


f(x) = 1, x>=0
     = 0, x<0


This is the simplest activation function, which can be implemented with a single if-else condition in python

def binary_step(x):
if x<0:
    return 0
    return 1
binary_step(5), binary_step(-1)

Output :


Step function is commonly used in primitive neural networks without hidden layer.

The binary step function can be used as an activation function while creating a binary classifier. But the function is not really helpful when there are multiple classes to deal with.
Moreover, the gradient of the step function is zero which causes a hindrance in the back propagation process. That is if you calculate the derivative of f(x) with respect to x, it comes out to be 0.

f'(x) = 0, for all x


In this article at OpenGenus, we have discussed about neural networks and activation functions in brief and also about binary step function, its uses and its disadvantages.

Binary Step Function
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