Dr. C. Shannon

Information Entropy

The information entropy (a.k.a Shannon’s Entropy) describes the disorder of the system. Let’s consider coin flipping system, where there are two possibilities for output such as head or tail. Hence, we may consider the system with 1-bit information (e.g. “0” for head and “1” for tail) and there is %50 chance for both of them. Yet, what if the coin’s density was not uniform ? or what if the coin was tricky ? Here, we can’t talk about %50 chance for both sides because one of the sides would have more chance to coincide. Thus, tricky coin would decrease the disorder due to fraudulent side would increase the chance to coincide. As a result, we can say that entropy of the system (tricky coin flipping) is going to decrease (e.g. entropy of the coin -that always coincides tail- is zero). 

Mathematical Representation of Shannon Entropy 

Self-Information of an Event:

I(x) = -logP(x) = log(1/P(x))

Shannon Entropy General Formula:

Binary (“0” and “1”):

In order to make a more precise definition in terms of computer science, entropy is the number of bits (binary) we can encode. Lets take a look at example:

How many binary we need to encode for months ?

log 2 12 = 3.58 , here 0.58 doesn’t represent a bit -computers operate discrete math- hence, we would need 4 bits for encoding process.

January (0000), February (0001), March (0010), April (0011), May (0100), June (0101), July (0110), August (0111), September (1000), October (1001), November (1010), December (1011). 

Entropy & Uncertainty 

Entropy is often used with the term “uncertainty” in data security. Uncertainty is the situation that makes a difference in a message and uncertain for the attacker.

Let’s store female(str) and male(str) in our database. Then, let our encrypted message be “kwét”. If an attacker finds a single bit from this message, the attacker can access the held information, i.e. if attacker finds out that the 1st bit is the “m” then attacker figure out the secret message is “male”. Hence, this situation uncertainty is 1 bit. Any known 1 bit from encrypted message can bring the secret message into open.

O.S. Tapsin

Resources: https://towardsdatascience.com/the-intuition-behind-shannons-entropy-e74820fe9800 —— https://medium.com/activating-robotic-minds/demystifying-entropy-f2c3221e2550 —— http://bilgisayarkavramlari.sadievrenseker.com/2008/12/17/entropi-entropy/

6 thoughts on “Information Entropy (Simplified)

  1. Good morning

    My name is Sergey and I am a founder of Sweaty Quid Freelancer Market place where you are able to buy and sell all types of online solutions varying from back links and guest post to explainer video clips, infographics and blog posts for your web site.

    I believe that you and cryptoquantus.com can seriously benefit from Sweaty Quid, whether you wish to provide your services or employ the services of freelancers to assist you to expand your company.

    I have been a freelancer on numerous marketplaces for in excess of 5 years and have had my accounts randomly shut down, my revenues pocketed and I simply had a hard time with lots of low quality freelancers. After much unnecessary aggravation, I decided to start my very own freelance market place that would do things in a different way and much better.

    After almost one year of caffeinne powered evenings, myself and my team at Creative Bear Tech have developed Sweaty Quid from ground up. One month into our release we have managed to attract a pretty good variety of top-notch freelancers and an extremely high number of repeat buyers. I believe this serves as a testament to our success.

    Sweaty Quid is a spam-free and transparent marketplace for quality freelancers and buyers. We are rigorously banning all spammy sellers who do not pass our quality threshold and leave only the very best ones. Keeping abreast of the most recent technologcal transformations, we also accept cryptocurrency as one of our payment methods. Our ethos that defines us is that sometimes less is more, primarily when it comes to quality freelancers.

    We are still very new in contrast to other freelance marketplaces, but we are already punching above our weight.

    I would love to welcome you personally to sign up with Sweaty Quid Freelancer Marketplace!

    Kind regards

    Sergey Greenfields
    Co-Founder of Sweaty Quid Freelancer Marketplace
    Flat 9, 1 Jardine Rd, St Katharine’s & Wapping,
    London E1W 3WD, United Kingdom


  2. Hi,

    I hope you are safe and healthy 🙂

    I’m reaching to write a guest article on your own website and will send you some topics for that.

    In case my ideas interest you, then I will send a post on any one of the topics chosen by you. The article is going to be of terrific quality and is free of cost.

    I’d just need you to provide me a backlink within the article. Looking forward to a reply.

    Thank you!


    Kristel Marquez


  3. Oh my goodness! an incredible article dude. Thanks However I am experiencing difficulty with ur rss . Don’t know why Unable to subscribe to it. Is there anybody getting an identical rss downside? Anyone who is aware of kindly respond. Thnkx


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s