There are 4 main types of number systems, Binary, Octal, Decimal and Hexadecimal. In this blog, we will have a look at those different number systems.

Before learning about the other number systems, let's first try to represent numbers in a different way, using what we all have learnt.

let's consider a number 3561 (randomly chosen), its expanded form will be

this can also be written as

or

did you observe the same thing which I did? while going from right to left (←) the power of 10 is increasing, interesting. Also, the number which is raised to different powers (10⁰, 10¹, 10², 10³… in this case) is the base.

The Decimal Number System

This is the system with which we all are familiar. The Decimal Number system has a range of 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) using those digits any number can be formed, the base for the Decimal number system is 10.

The Binary Number system

The Binary Number system has a range of 2 digits (0, 1), this is the system that computer uses as it can be represented digitally, 0 as a low signal and 1 as a high signal, let's have a look at an example, decimal 13

The RHS is equal to 1 × 8 + 1 × 4 + 0 × 2 + 1 × 1, which is 8 + 4 + 1 = 13.

The Octal Number System

The Octal Number system has a range of 8 digits (0, 1, 2, 3, 4, 5, 6, 7), this system has a base of 8. For example decimal number 89

The RHS is equal to 1 × 64 + 3 × 8 + 1 × 1, which is 64 + 24 + 1 = 89.

The Hexadecimal Number System

The hexadecimal number system has a range of 16 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F), you will find yourself using this system when working with colours, white in hex (hexadecimal) is FFFFFF (first 2 places for the value of red which is 255, next 2 for blue which is 255, and the last 2 values for green which is also 255). Let’s try to convert decimal 209 to Hexadecimal, we can write 209 as (13 × 16 + 1 × 1), rewriting this will give us (D = 13, in hex):-

here is a table that has values from 0–15 written in all 4 Number systems discussed in this blog, as an exercise try to understand it and convert the value from one system to another.

That’s all for This blog, Have a great day Ahead!

Yash

Hello!,

Yash here, and this is the place where I share my learnings with you all.

If you have not read my previous blog make sure to check that blog out to get a basic understanding of logarithms.

we will be covering the following properties of logarithms:-

• The Product Rule
• The Quotient Rule
• The Power Rule
• The Change of the Base Rule

let’s get started!

The Product Rule

This is a different way of representing the product rule of exponents

product rule of exponents: aᵐ * aⁿ = aᵐ⁺ⁿ

if you are adding two logs of the same base, the result will be the log (with the same base) and the argument as the product of arguments of given logs…

The Quotient Rule

This is also just a different way of writing the quotient rule of exponents

[ quotient rule of exponent:

aᵐ / aⁿ = aᵐ⁻ⁿ ]

If you are subtracting 2 logs with the same base the resulting log will be the log (of the same base) with the argument as the quotient of the arguments of the original logs…

The Power Rule

By multiplying a constant a with log with base b and argument c is equal to log with base b and argument as c to the power a.

The Change of the Base Rule

The change of the base rule allows, you to calculate any log… many calculators do not allow you to have a different base, so by using this formula calculating the log of any base is made easy.

That’s all for this blog.

Until next time, Have a great day ahead!

Yash

I recently learnt about logarithms, they seem fun, so I decided to share what I have learnt with you all.

before having a look at what they are, lets first have a look at some of their real-life applications:-

• The pH scale in chemistry is logarithmic.
• The Richter Scale used to measure earthquake is logarithmic.
• The economy is also measured on a logarithmic scale.
• The spacing between the guitar frets.

if you want to understand the scale make sure to check out this video by Khan Academy after you complete reading this blog.

So What are Logarithms?

after googling the first answer I got is:-

A logarithm is a mathematical operation that determines how many times a certain number, called the base, is multiplied by itself to reach another number. Because logarithms relate geometric progressions to arithmetic progressions.

let's try to break it down, “how many times a certain number, called the base is multiplied by itself”, this sounds familiar, it is exponents (baseᵉˣᵖ),

if we compare the expression of the logarithm with that of exponents, we see that it's just a new way to write the same thing. Let me give you an example of a log using numbers instead of variables.

There are some restrictions on the number (argument to the log function) and the base, those are:-

• The number cannot be negative, if the number (argument) is negative the answer cannot be in real numbers.
• The base should be greater than 0, as, in an exponential function, the base is always defined to be positive.
• The base should not be 1, if the base is 1, we will not always get a definite answer, as 1ˣ for any value of x is 1.

we have some bases that are very common, writing the base always when writing the log function does not make sense, so we have defined some special logs, namely log base 10, and natural log (log base e).

In my next blog, we will have a look at some properties of logarithms.

Until next time, Have a great day ahead!

Yash

Let us have a look at what we will be covering:-

[
    Reading the errors,
    Trying to search for the error on the internet,
    Using forums and communities
]

ok, so first we need some code, the things we are covering, looks like a python list to me, let me create a file and add this list to that file, this is how my file looks like

when I try to run this, I get an error, let’s have a look at it

$ python error.py
 
File "/home/yashp/code/error.py", line 2
    Reading the errors,
            ^
SyntaxError: invalid syntax

let’s try to read what this error has to say. The last line which starts with the kind of error we have, here we have a SyntaxError which is followed by a message, which for us is invalid syntax meaning that we have some problem with our syntax, File "/home/yashp/code/error.py", line 2 means that in file error.py which is located in the folder /home/yashp/code contains the error on line number 2, we also see that it has printed line 2 for us, which is Reading the errors .

After inspecting line 2 of model.py I found out that I did not add quotes around the sentences to make them strings, which is to be stored in the list, so now I have added quotes around them, and it works as expected without any errors.

Let’s now take an example of another error

This is the code for the next example, the first cell downloads the following code as a model.py file.

after you run that notebook’s second cell you will receive a NotImplementedError. the complete error is as follows:-

let’s break this down, we see that the error is NotImplementedError, what does this mean? here is a link to an answer which defines NotImplementedError. and the error takes place at <ipython-input-2-8d64230b72fb> in <module>() which is nothing but the second cell of the notebook, and the error we have is on line 10 of the second cell, i.e. model(sample_data) .

on google colab after running that cell, and getting that error we can see that it has a button that says Search StackOverflow, after clicking on that you will be redirected to google which has results that look like this:

these results are from StackOverflow which is the first place you would like to visit for your error and also the main thing in the second point we are covering in this blog. instead of clicking that button, you can alternatively use search queries like “NotImplementedError StackOverflow” or “NotImplementedError PyTorch StackOverflow”, the 2nd result defines NotImplementedError for us, and the 4th result looks something similar to what we have if you check model.py you will see that this is similar but not what we want.

now we will try to search on the internet with the search query which is relevant to the error let’s try ‘NotImplementedError PyTorch’, we see that the 1ˢᵗ result is from StackOverflow, but the next ones are from PyTorch Forums, and the 2ⁿᵈ result says [SOLVED] so let’s have a look at that, after reading a few replies, we find that this reply by ptrblck says that it can be because of a typo or incorrect indentation, and we also find that in model.py forward is spelt incorrectly, we can just open this file and correct the spelling and run the cell again after restarting the kernel the error is no more there. (note: restarting the kernel is necessary, else python won’t load the changes else use the cached file, so we need to restart).

If with all these steps the error you are getting didn’t get solved you have Forums and communities to ask about your error, there are forums from the specific technologies themselves, like TensorFlow Forum, PyTorch Forum, fast.ai Forum and others. If it does not have a forum of itself you can ask on a more general forum/community like StackOverflow or others which you can find on discord/slack etc…

Summary:

• The error Traceback gives us the information about where the error is and what the error is.
• After identifying the error we should try to search about it on StackOverflow.
• If we didn’t find anything on StackOverflow we should just try googling about the error. Try to look for answers on forums.
• If the error is still not solved, ask on Forums (if possible official ones) and general communities.

Until next time, Have a great day ahead!.

Yash