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    <title>DEV Community: Sona Grigoryan </title>
    <description>The latest articles on DEV Community by Sona Grigoryan  (@sonagrigoryan2005).</description>
    <link>https://dev.to/sonagrigoryan2005</link>
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      <title>DEV Community: Sona Grigoryan </title>
      <link>https://dev.to/sonagrigoryan2005</link>
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    <item>
      <title>Introduction to Java (Java fundamentals, Data Types, Intro to OOP)</title>
      <dc:creator>Sona Grigoryan </dc:creator>
      <pubDate>Wed, 29 Nov 2023 16:30:28 +0000</pubDate>
      <link>https://dev.to/sonagrigoryan2005/introduction-to-java-java-fundamentals-data-types-intro-to-oop-1k1o</link>
      <guid>https://dev.to/sonagrigoryan2005/introduction-to-java-java-fundamentals-data-types-intro-to-oop-1k1o</guid>
      <description>&lt;p&gt;Hello everyone, today I am going to introduce you to the Java programming language. The topics that I am going to discuss today include:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;Java Fundamentals 
a. Compiled vs Interpreted languages 
b. Java as a compiled language
c. Java Virtual Machine
d. Java Development Kit &lt;/li&gt;
&lt;li&gt;Data Types in Java
a. Differences between Primitive and Non-Primitive Types
b. Primitive types
c. Non-Primitive Types&lt;/li&gt;
&lt;li&gt;Introduction to Object Oriented Programming
a. OOP
b. 4 pillars of OOP
1) Inheritance
2) Encapsulation
3) Abstraction
4) Polymorphism&lt;/li&gt;
&lt;/ol&gt;

&lt;p&gt;Let's start right away!&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;Java Fundamentals&lt;/li&gt;
&lt;/ol&gt;

&lt;p&gt;a) Compiled vs Interpreted languages.&lt;/p&gt;

&lt;p&gt;Programming languages can be compiled or interpreted. &lt;br&gt;
In compiled languages the whole program is translated to machine code and than executed by the processor while in Interpreted languages the program is executed directly without being compiled first. Interpreted programs run slower than the compiled program. Additionally, since the programs in compiled languages are translated first into machine code, which is specific to the architecture of the computer, the compiled programs can only be run on the computers they were compiled on.&lt;br&gt;
Some exampled of compiled and interpreted languages.&lt;br&gt;
Compiled languages : C++, Java, etc.&lt;br&gt;
Interpreted languages : JavaScript, Python, etc.&lt;/p&gt;

&lt;p&gt;b) Java as a compiled language&lt;/p&gt;

&lt;p&gt;Java is a compiled language, but since it is platform independent (I will talk about this in a little but) the compilation is executed in two stages instead of one, where first the code is translated to Java bytecode and later run and executed through JVM (again will be discussed later in the post).&lt;/p&gt;

&lt;p&gt;c) Java Virtual Machine&lt;/p&gt;

&lt;p&gt;At first Java was designed to be run on a specific OS, but that proved to be a problem. Later JVM (Java Virtual Machine) was created. With the help of JVM the Java code can be executed on any platform if there is JVM installed. To conclude let's say that JVM has two primary functions: 1. to allow Java programs to run on any device or operating system (known as the "write once, run anywhere" principle) and 2. to manage and optimize program memory.&lt;/p&gt;

&lt;p&gt;d) Java Development Kit &lt;/p&gt;

&lt;p&gt;IF you want to develop and run a software application in Java, you will need to install JDK (Java Development Kit). This is the overall composition of JDK:&lt;/p&gt;

&lt;p&gt;&lt;a href="https://media.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2F14qfeoerquybunel5fv3.jpg" class="article-body-image-wrapper"&gt;&lt;img src="https://media.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2F14qfeoerquybunel5fv3.jpg" alt="Image description"&gt;&lt;/a&gt;&lt;/p&gt;

&lt;p&gt;JDK contains some Developments Tools to help you and JRE (Java Runtime Environment) to execute the code. JRE in turn contains the JVM and some classes libraries to help with the development. If you have a simple program and not a software application it is enough to download the JRE without downloading the whole JDK.&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;Data Types in Java&lt;/li&gt;
&lt;/ol&gt;

&lt;p&gt;a) Primitive vs Non-Primitive Types&lt;/p&gt;

&lt;p&gt;I will list the characteristics of first Primitive types and than Non-primitive types. The points are structured as contrasting, and so highlight the core differences.&lt;/p&gt;

&lt;p&gt;Primitive Types&lt;/p&gt;

&lt;p&gt;. Primitive types store simple values directly.&lt;br&gt;
. They are predefined by the language and not composed of other types.&lt;br&gt;
. They have a fixed size in memory.&lt;br&gt;
. A primitive type has always a value.&lt;br&gt;
. Primitive types cannot be used to call methods to perform certain operations&lt;br&gt;
. A primitive type starts with a lowercase letter.&lt;/p&gt;

&lt;p&gt;Non-primitive (reference) Types&lt;/p&gt;

&lt;p&gt;. Reference types are more complex and are composed of primitive or other reference types.&lt;br&gt;
. they can dynamically grow or shrink in size (e.g., with ArrayList)&lt;br&gt;
. non-primitive types can be null.&lt;br&gt;
. Non-Primitive types can be used to call methods to perform certain operations&lt;br&gt;
. non-primitive types start with an uppercase letter.&lt;/p&gt;

&lt;p&gt;b) Primitive types &lt;/p&gt;

&lt;p&gt;byte&lt;br&gt;
8-bit signed integer (-128, 127)&lt;br&gt;
short&lt;br&gt;
16-bit signed integer (-32768, 32767)&lt;br&gt;
int&lt;br&gt;
32-bit signed integer (-2^31, 2^31-1)&lt;br&gt;
long&lt;br&gt;
64-bit signed integer (-2^63, 2^63-1)&lt;/p&gt;

&lt;p&gt;Example: 745963&lt;/p&gt;

&lt;p&gt;All the types above are used to represent integers, however the amount of memory they take is different, hence the value range is different for each of them.&lt;/p&gt;

&lt;p&gt;float&lt;br&gt;
32-bit floating-point.&lt;br&gt;
double&lt;br&gt;
64-bit floating-point.&lt;/p&gt;

&lt;p&gt;Example: 1.00713&lt;/p&gt;

&lt;p&gt;The types above are used to represent floating point numbers and depending on the type reserve different amount of memory.&lt;/p&gt;

&lt;p&gt;char&lt;br&gt;
16-bit Unicode character.&lt;/p&gt;

&lt;p&gt;Example:   ‘s’    ‘@’&lt;/p&gt;

&lt;p&gt;The char type is used to represent the Unicode characters (from letters to symbols) and take up 16 bits in the memory.&lt;/p&gt;

&lt;p&gt;boolean&lt;br&gt;
unsigned 8 bits representing true or false values&lt;/p&gt;

&lt;p&gt;Example:  true, false&lt;/p&gt;

&lt;p&gt;The boolean is used to in programing to represent true and false values. True and false are the only values that boolean can take.&lt;/p&gt;

&lt;p&gt;c) Non-primitive types&lt;/p&gt;

&lt;p&gt;For Non-primitive types I will only discuss Strings, Arrays and Classes, but there are many other types for example Interface, ArrayList, etc.&lt;/p&gt;

&lt;p&gt;String:&lt;/p&gt;

&lt;p&gt;Strings is a collection of char-s (characters).&lt;/p&gt;

&lt;p&gt;Example:&lt;br&gt;
“Hello, world!”&lt;/p&gt;

&lt;p&gt;Array:&lt;br&gt;
Array is an ordered, enumerated collection of elements. However in Java, Arrays only can contain one type of elements, that is can be all Strings, ints, Arrays, etc. In programming the elements of an Array get unique numbers (indexes) and the count starts from 0 instead of 1.&lt;/p&gt;

&lt;p&gt;Example:&lt;br&gt;
[“school”, “search”, “sun”]&lt;br&gt;
[1130, 613, 528, 304]&lt;/p&gt;

&lt;p&gt;Example:&lt;br&gt;
        0     1    2    3&lt;br&gt;
arr = [1130, 613, 528, 304]&lt;br&gt;
arr[2] = 528&lt;/p&gt;

&lt;p&gt;Classes:&lt;/p&gt;

&lt;p&gt;A class is an abstract blueprint that creates more specific, concrete objects. Classes often represent broad categories, like Dog or Human or Chair, that share attributes. These classes define what attributes an instance of this type will have, like color. Additionally classes can also contain methods that perform some action and are specific only to that object.&lt;/p&gt;

&lt;p&gt;Example:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;Class Marker {
    String color = “blue”;
    write (text){}
}

Marker MyMark = new Marker();
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;In this example we first defined the class of Marker and than created a new instance of these class (object).&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;Introduction to OOP&lt;/li&gt;
&lt;/ol&gt;

&lt;p&gt;a) OOP&lt;/p&gt;

&lt;p&gt;Object-Oriented Programming (OOP) is a programming paradigm in computer science that relies on the concept of classes and objects. It is used to structure a software program into simple, reusable pieces of code blueprints (called classes), which are used to create individual instances of objects.&lt;/p&gt;

&lt;p&gt;Basically, in OOP languages the complex code is divided into simple, reusable parts (classes) to help structure the program.&lt;/p&gt;

&lt;p&gt;b) 4 pillars of OOP&lt;/p&gt;

&lt;p&gt;These are some concepts that is important to understand when we talk about OOP.&lt;/p&gt;

&lt;p&gt;1) Inheritance&lt;/p&gt;

&lt;p&gt;Inheritance allows a class (subclass) to inherit the properties and behaviors of another class (superclass).&lt;/p&gt;

&lt;p&gt;Let's look at the example to understand better:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;Class Dog {
    int numOfLegs = 4;
    String color = “black”;
    bark (){}
}

Class Hasky extends Dog{
    String color = “white”;
    pullsled(){}
}

&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;When we want to create a new class that should share the same attributes and methods of some other class to avoid repeating the same code twice we can extend the new class to an already existing parent class and so, inherit all it's properties and methods. We can overwrite those attributes if they are different for the child class, or we can add some new attributes and methods in addition to the inherited ones.&lt;/p&gt;

&lt;p&gt;2) Encapsulation&lt;/p&gt;

&lt;p&gt;Encapsulation is the bundling of data and methods that operate on the data into a single unit known as a class.&lt;/p&gt;

&lt;p&gt;Encapsulating means that we are isolating some piece of code in a class and this allows us to first make the code simpler and second to make our code more secure. In classes we can specify if we want the attribute or method to be public (accessibly outside of the class) or private (only accessibly inside the class).&lt;/p&gt;

&lt;p&gt;Here is an example to better understand encapsulation.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;Class Car {
    public String color = “white”;
    public int milesDriven = 10000;
    public stir(){}
    private engineWork() {}
}
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;3) Abstraction&lt;/p&gt;

&lt;p&gt;Abstraction involves simplifying complex systems by modeling classes based on the essential properties and behaviors they share. It focuses on what an object does rather than how it achieves its functionality.&lt;/p&gt;

&lt;p&gt;Basically to  make the User Interface as simple as possible some pieces of code that we are not interested in can be abstracted away and so kind of hided. It is still accessible, but to make everything easier it is hided behind a more simple interface.&lt;/p&gt;

&lt;p&gt;Here is and example:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;Class ParkingLot {
      checkin() {}
      checkout(){
            calculateFee(){}
            cleanSpot(){}
     }
}
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Here in these example calvulateFee() and cleanSpot() is abstracted away since we do not need to necessarily engage with each one of them individually.&lt;/p&gt;

&lt;p&gt;4) Polymorphism &lt;/p&gt;

&lt;p&gt;Polymorphism allows objects of different classes to be treated as objects of a common base class. It enables a single interface to represent different types or forms.&lt;/p&gt;

&lt;p&gt;Let's look at the example below:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;Class Marker {
    String color = “green”;
    draw(geomObject){}
}
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Objects like triangle, circle, square can all be passed to these function. It is possible, even though they belong to different classes, because they all share some common properties and belong to a common base class.&lt;/p&gt;

&lt;p&gt;This is all, thank you all for reading, I hope it was helpful to you!&lt;/p&gt;

</description>
      <category>java</category>
      <category>oop</category>
    </item>
    <item>
      <title>Binary Numbers (different number bases, conversions and mathematical operations)</title>
      <dc:creator>Sona Grigoryan </dc:creator>
      <pubDate>Wed, 13 Sep 2023 22:36:18 +0000</pubDate>
      <link>https://dev.to/sonagrigoryan2005/binary-numbers-different-number-bases-conversions-and-mathematical-operations-15jo</link>
      <guid>https://dev.to/sonagrigoryan2005/binary-numbers-different-number-bases-conversions-and-mathematical-operations-15jo</guid>
      <description>&lt;p&gt;Today we are going to learn about different number bases, binary numbers, conversation from one base to another one and also we will learn how to do mathematical operations with different base numbers. &lt;/p&gt;

&lt;p&gt;I will also provide the link to my video about binary numbers.[Binary numbers video].(&lt;a href="https://youtu.be/PbpHM63TCA8?si=wR9zLHoQ6iead2E3"&gt;https://youtu.be/PbpHM63TCA8?si=wR9zLHoQ6iead2E3&lt;/a&gt;)&lt;/p&gt;

&lt;p&gt;1) What are Binary Numbers? &lt;/p&gt;

&lt;p&gt;Binary numbering system uses only two digits to represent numbers. Those digits are 0 and 1. Binary numbers are mostly used in programming and computer science, so learning binary numbers is very important in order to succeed in your profession. 1is considered the state when  electricity flows and 0 when no electricity flows. Imagine a box, and though that box electricity flows. And that box has to either let the electricity flow or block the way. So that is how we can get those 2 digits in computers. Those small boxes are called transistors and also bits ( places to store either 1 or 0). For example 1011 is a binary number and it is the same as 11 in our numbering system which is base ten or decimal. One more important thing to note. Based on the number of bits we have we can store up to different numbers in binary. For example, when we have 2 bits we the highest number possible to represent is 3 and the amount of numbers that can be expressed will be 4. The formula is the following. &lt;/p&gt;

&lt;p&gt;The highest number: 2^n - 1&lt;br&gt;
Amount of all possible numbers: 2^n &lt;/p&gt;

&lt;p&gt;2) Different Base Numbers &lt;/p&gt;

&lt;p&gt;So when I say base 2 or base 10 or base 16, etc, what does that mean? The number shows how many digits are used in that particular numbering system. For example, as we already said, binary or base 2 uses 2 digits, decimal or base 10 uses 10 digits 0-9. So you might ask what about base 16, for example? Well since there are not enough digits created to represent 16 different numbers, ifor base 16 and many other bases letter are used. So: &lt;/p&gt;

&lt;p&gt;11 - A&lt;br&gt;
12 - B&lt;br&gt;
13 - C&lt;br&gt;
14 - D&lt;br&gt;
15 - E &lt;/p&gt;

&lt;p&gt;As I said binary is used in computerers. Base 8 is also used. And base 16? Base 16 also has many usages, but probably the most important one is colors. To specify the color we use hex code or base 16 numbers. &lt;/p&gt;

&lt;p&gt;3) other bases to base 10 &lt;/p&gt;

&lt;p&gt;I will only consider one example of base 2 to base 10, but other conversions are done by the same logic. &lt;/p&gt;

&lt;p&gt;Let's take 11101 as our binary num. &lt;/p&gt;

&lt;p&gt;So we write the number &lt;/p&gt;




&lt;h2&gt;
  
  
  11101
&lt;/h2&gt;

&lt;p&gt;And  then assign ranks to them from right to left.&lt;/p&gt;

&lt;p&gt;----------‐------------&lt;br&gt;
4       3     2       1     0    &lt;/p&gt;

&lt;h2&gt;
  
  
  1    1    1    0    1
&lt;/h2&gt;

&lt;p&gt;Then we take those rank and take 2 to the power of that number and multiply by the digit  and them all together. &lt;/p&gt;

&lt;p&gt;----------‐------------&lt;/p&gt;

&lt;p&gt;    1              1                 1             0             1&lt;br&gt;
1×2^4  +  1×2^3 +  1×2^2 +  0×2^1 +  1×2^0 &lt;/p&gt;




&lt;p&gt;And after calculating we get 29 which is this binary number in decimal form.&lt;/p&gt;

&lt;p&gt;The reason we rewrite that two is because we are converting from base 2 which has 2 digits. So If we were to convert from base 4 we would write 4 instead of that 2 and if from base 16, we would have written 16 instead of 2. And in base 16 since the form is with letters when following the formula we should take the corespondant number instead of the letter.numbers. &lt;/p&gt;

&lt;p&gt;4) base 10 to other bases &lt;/p&gt;

&lt;p&gt;Again I will only do the example on binary, but the principle is teh same and you can easily do the same for other bases. &lt;/p&gt;

&lt;p&gt;Let's take 87 and concert it to binary. &lt;/p&gt;




&lt;h2&gt;
  
  
  87
&lt;/h2&gt;

&lt;p&gt;The way to get tje binary number is to divide this number (87) by 2(because we want to convert to base 2) and get all the remainders which will construct our binary number. Now let's see on the example. &lt;/p&gt;

&lt;p&gt;So we have 87 &lt;/p&gt;

&lt;p&gt;-‐-----------------------&lt;br&gt;
87 | 1&lt;br&gt;
43 |&lt;br&gt;
‐----------------------- &lt;/p&gt;

&lt;p&gt;1 here is the remainder and 43 is the result which we will gain devide by two the &lt;br&gt;
Same way. &lt;/p&gt;

&lt;p&gt;-‐-----------------------&lt;br&gt;
87 | 1&lt;br&gt;
43 | 1&lt;br&gt;
21 | 1&lt;br&gt;
10 | 0&lt;br&gt;
5   | 1&lt;br&gt;
2   | 0&lt;br&gt;
1   | 1&lt;br&gt;
0   | &lt;br&gt;
‐----------------------- &lt;/p&gt;

&lt;p&gt;Now so as you see we continue until we've reached 0. To get the binary number, we take those remainders from bottom to the top and there is our number.&lt;br&gt;
In this example it is: 1010111 which is the binary representative of the 87.&lt;/p&gt;

&lt;p&gt;5) operations with different bases &lt;/p&gt;

&lt;p&gt;Operation with various bases works similarly to decimal numbers. Today I will only cover addition and multuplication for base 2 and base 4. &lt;/p&gt;

&lt;p&gt;Addition &lt;/p&gt;

&lt;p&gt;So let's do first binary.&lt;br&gt;
Let's take 1011 + 11101&lt;/p&gt;

&lt;p&gt;-‐----------------------‐-----------------------&lt;br&gt;
01011&lt;br&gt;
11101&lt;br&gt;
-‐---------------------------------------------- &lt;/p&gt;

&lt;p&gt;As you see you can add 0 from the left end that new number will be equale to or number, the value won't change. &lt;/p&gt;

&lt;p&gt;So let's add&lt;/p&gt;

&lt;p&gt;‐----------------------‐-----------------------&lt;br&gt;
01011&lt;br&gt;
11101&lt;/p&gt;




&lt;p&gt;         0          carry 1 &lt;br&gt;
-‐----------------------------------------------&lt;br&gt;
        &lt;br&gt;
First column  1 plus 1 we get 10 in binary so we write 0 and carry one over just like we do in decimals.&lt;/p&gt;

&lt;p&gt;‐‐----------------------‐-----------------------&lt;br&gt;
01011&lt;br&gt;
11101&lt;/p&gt;




&lt;p&gt;       00     carry 1&lt;br&gt;
-‐---------------------------------------------- &lt;/p&gt;

&lt;p&gt;Second column got 1 + 0 = 1 but we also have 1 carried over so it becomes 1 + 1 again and so we write 0 and carry one over &lt;/p&gt;

&lt;p&gt;‐‐----------------------‐-----------------------&lt;br&gt;
01011&lt;br&gt;
11101&lt;/p&gt;




&lt;p&gt;    000     carry 1&lt;br&gt;
-‐----------------------------------------------&lt;/p&gt;

&lt;p&gt;Same thing in the third column as in the second.&lt;/p&gt;

&lt;p&gt;‐‐----------------------‐-----------------------&lt;br&gt;
01011&lt;br&gt;
11101&lt;/p&gt;




&lt;p&gt;  1000     carry 1&lt;br&gt;
-‐---------------------------------------------- &lt;/p&gt;

&lt;p&gt;In the fourth column we already have three ones ( 2 initial and one carried over). So from first two ones we get 10 (write 0, carry 1 over) and then add  and get 1 in tat column. &lt;/p&gt;

&lt;p&gt;‐‐----------------------‐-----------------------&lt;br&gt;
01011&lt;br&gt;
11101&lt;/p&gt;




&lt;p&gt;101000     &lt;br&gt;
-‐---------------------------------------------- &lt;/p&gt;

&lt;p&gt;In the next column we have the same thing one 1 and another 1 carried over so we get 10 and since there are no more columns we can write that 10.&lt;/p&gt;

&lt;p&gt;Multiplication &lt;/p&gt;

&lt;p&gt;Let's take 1101 × 1111 &lt;/p&gt;

&lt;p&gt;So again the same way as decimals. &lt;/p&gt;

&lt;p&gt;‐‐----------------------‐-----------------------&lt;br&gt;
               1101&lt;br&gt;
               1111&lt;br&gt;
             _______&lt;br&gt;
               1101&lt;br&gt;
            1101&lt;br&gt;
          1101&lt;br&gt;
       1101&lt;br&gt;
   _____________ &lt;/p&gt;

&lt;p&gt;-‐---------------------------------------------- &lt;/p&gt;

&lt;p&gt;And then we add all of those together.&lt;/p&gt;

&lt;p&gt;‐----------------------‐-----------------------&lt;br&gt;
               1101&lt;br&gt;
               1111&lt;br&gt;
             _______&lt;br&gt;
               1101&lt;br&gt;
            1101&lt;br&gt;
          1101&lt;br&gt;
       1101&lt;br&gt;
   _____________&lt;br&gt;
                    11&lt;br&gt;
-‐----------------------------------------------&lt;/p&gt;

&lt;p&gt;---------------------‐-----------------------&lt;br&gt;
               1101&lt;br&gt;
               1111&lt;br&gt;
             _______&lt;br&gt;
               1101&lt;br&gt;
            1101&lt;br&gt;
          1101&lt;br&gt;
       1101&lt;br&gt;
   _____________&lt;br&gt;
                 011      carry 1 &lt;br&gt;
-‐----------------------------------------------&lt;/p&gt;

&lt;p&gt;---------------------‐-----------------------&lt;br&gt;
               1101&lt;br&gt;
               1111&lt;br&gt;
             _______&lt;br&gt;
               1101&lt;br&gt;
            1101&lt;br&gt;
          1101&lt;br&gt;
       1101&lt;br&gt;
   _____________&lt;br&gt;
              0011  carry 1 over (×2)&lt;br&gt;
-‐----------------------------------------------&lt;/p&gt;

&lt;p&gt;---------------------‐-----------------------&lt;br&gt;
               1101&lt;br&gt;
               1111&lt;br&gt;
             _______&lt;br&gt;
               1101&lt;br&gt;
            1101&lt;br&gt;
          1101&lt;br&gt;
       1101&lt;br&gt;
   _____________&lt;br&gt;
            00011  carry 1 over (×2)&lt;br&gt;
-‐----------------------------------------------&lt;/p&gt;

&lt;p&gt;---------------------‐-----------------------&lt;br&gt;
               1101&lt;br&gt;
               1111&lt;br&gt;
             _______&lt;br&gt;
               1101&lt;br&gt;
            1101&lt;br&gt;
          1101&lt;br&gt;
       1101&lt;br&gt;
   _____________&lt;br&gt;
         000011  carry 1 over (×2)&lt;br&gt;
-‐----------------------------------------------&lt;/p&gt;

&lt;p&gt;---------------------‐-----------------------&lt;br&gt;
               1101&lt;br&gt;
               1111&lt;br&gt;
             _______&lt;br&gt;
               1101&lt;br&gt;
            1101&lt;br&gt;
          1101&lt;br&gt;
       1101&lt;br&gt;
   _____________&lt;br&gt;
       110000011  carry 1 over (×2)&lt;br&gt;
-‐----------------------------------------------&lt;/p&gt;

&lt;p&gt;The addition works the same way as we wearied before so I believe you will be able to do the multilication. &lt;/p&gt;

&lt;p&gt;Thank you for reading the entire post and I hope I was able to help you. &lt;/p&gt;

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