 Hello friends, I am Sanjay Gupta. I welcome you on my YouTube channel. My YouTube channel contains more than 800 videos. You can search these videos through the keyword programming by Sanjay Gupta. All these videos are related to computer programming. So you can learn various programming languages by following my YouTube channel. You can connect with me for any kind of queries using my email ID or WhatsApp number. In this video, I am going to discuss about conversion from binary, octal and hexadecimal to decimal number system. So we are going to learn how we can convert binary, octal and hexadecimal number systems into decimal number systems. So first we are going to learn about the steps. So here you can see three steps are available. So first step says determine the column or positional value of each digit depending on the position of the digit and the base of the number system. Second point says multiply the obtained column values by the digits in the corresponding columns. And third says sum the product calculated in step two. This is the equivalent value in decimal. So first I am going to discuss about conversion of integer numbers. So this is the first example where I am going to convert binary number system to decimal number system. And the question says we have to convert this number. 11001 its base is 2. That's why it is binary and we have to convert it into decimal. So here you can see base is written as 10. So now we have to follow those three steps. So first we have to identify the positions. So here you can see this type most digit that is one its position is zero. Then zeros position is one. Then next zero is available at position two. Then one is available at position three and another one is available at position number four. So again going back to the steps. So here you can read it again determine the column value of each digit depending on the position of the digit. So we have identified the position of the digit and their positional value and the base of the number system. So we have identified both things. So these are the position values and base of number system is two. Now next step says multiply the obtained column values by the digits in the corresponding columns. So here you can see I am multiplying this digit one with two raised four. So base is two and position value of this digit one is four. You can see it is written here. So does it is one which is multiplied by two raised four to is the base and four is the position value. Similarly, next does it one is multiplied with two raised three. Then zero is multiplied with zero is sorry two raised two then zero into two raised one then one into two raised zero. So this way all the multiplications are available here. Now again I am moving back to the steps. Third step says some of the products calculated in step two and this will be the equivalent value in decimal. So now we have to add all these results. So here you can see the addition value is available 16 plus 8 plus 0 plus 0 plus 1 and the final result is 25 whose base is 10. So here you can say the conversion of 1 1 0 0 1 which is a binary number. It's decimal equivalent is 25. So I hope you have understood how we can identify the positions of the digits their position values. How we can multiply those digits with the position values along with the base and how we can add the multiplication results so that we can find the final result. So after learning conversion from binary to decimal. Now I'm going to discuss about conversion of octal number to decimal number. So here you can see the value which we have to convert is 4706 whose base is octal. We have to convert it into decimal. So base will be 10. Now again we have to identify the position. So here you can see position of 6 is 0 then position of 0 is 1 position of 7 is 2 position of 4 is 3. So this way I have identified the positions. Now I have to multiply a particular digit visits position along with base. So here position is 4 which is multiplied with 8 raised 3. So here 8 is the base of the number and 3 is its position. So 8 raised 3 is multiplied with 4. Similarly 7 is multiplied with 8 raised 2 0 is multiplied with 8 raised 1 and 6 is 6 is multiplied with 8 raised 0. And finally their multiplication are added and the final result will be 2502 and its base is 10. So you can say 4706 which is an octal number. Its decimal equivalent value is 2502 that is written at the bottom of this slide. So it is easy to convert octal to decimal with the same formula as we converted binary to decimal. Same formula will be used for conversion from hexadecimal number to decimal number. So here you can see the number is 1 AC which is hexadecimal number. Its base is 16 and we have to convert this number into decimal. So again we have to identify the positions. So here C is available at position 0. A is available at position 1 and 1 is available at position 2. And you can see A can be represented as 10 and C can be represented as 12. Because for calculation purpose we can't use A directly. We have to convert it into 10. So now you can see here I am using this digit with its position value. So 1 is multiplied with 16 raise to. So 16 is the base and position of the digit 1 is 2. That's why it is multiplied with 16 raise to. Then capital A which is converted into 10 is multiplied with 16 raise 1. And similarly C which is converted into 12 is multiplied with 16 raise 0. And their multiplication results are added. So final outcome is 428. So you can see the conversion result of hexadecimal number that is 1 AC. And it is converted into decimal. So its decimal equivalent is 428. So I hope you have understood how we can convert integer numbers that are available in binary, octal and hexadecimal numbers into decimal number system. Now after learning conversion of integer numbers. Now I am going to discuss about conversion of fractional numbers. So we will be using the same set of steps for converting fractional numbers. From binary to decimal from octal to decimal and from hexadecimal to decimal. So first I am going to convert binary to decimal. So let's take an example. Here values written as 1 1 1 0 0 1 point 1 1 0 1. So it is a binary number which we need to convert into decimal. So here you can see for the values which are available at left hand side of this decimal point. Their positions are 0 1 2 3 4 5 and the values which are available at right hand side of this decimal point. Their positions are minus 1 minus 2 minus 3 and minus 4. If we have more digits then we can extend these position values as minus 5 minus 6 and so on. So this is the positional values. Now here you can see for left most digit that is 1. It is multiplied with 2 raised 5. So 2 is the base value here and 5 is the position value. So 1 is multiplied with 2 raised 5 so that we can find out its outcome. Similarly other values are multiplied. Here you can see 1 into 2 raised minus 1. So this is for this set of digit. So here 1 is the digit and its position value is minus 1. So that's why the equation will be 1 into 2 raised minus 1. And similarly all other digits are multiplied with their positional values. Then their multiplication results are added to find out the final outcome. So final outcome is 57.8125. So you can say 111001.1101. It is a binary number and its decimal equivalent is 57.8125. So this is the example which is converting fractional value from binary to decimal. Now we have to use same set of steps to convert octal number system value into decimal number system. So here you can see number is 12.36 which is an octal. We have to convert it into decimal. Here you can see the position values are identified. These position values are both for value which is available at left hand side of decimal point as well as values which are available at right hand side of decimal point. So for left hand side we have positive numbers 01. For right hand side we have negative numbers minus 1 and minus 2. And similarly you can see the multiplication values. These are for 1 and 2. These digits and then these two equations for these two digits 3 and 6. So 3 and 6 are multiplied with negative powers and 1 and 2 are multiplied with positive powers. And these multiplication results are added to frame the final outcome. So final outcome is 10.46875. So you can say 12.36 is an octal number. Its equivalent decimal number is 10.46875. And lastly, now I'm going to convert hexadecimal number into decimal number. So this is hexadecimal number 12.36. I have to convert it into decimal number. So again we have to identify the positions. So here you can see the position values are identified. Then these positions are multiplied with base value along with the power. So 1 is multiplied with 16 raised 1. 2 is multiplied with 16 raised 0. 3 is multiplied with 16 raised minus 1. And 6 is multiplied with 16 raised minus 2. And these multiplication results are added to frame the final outcome. So here you can see final outcome is 18.2109375. So the original number was 12.36 which is hexadecimal number. Its equivalent decimal number is 18.2109375. So this way I demonstrated you how we can convert integer and fractional numbers from binary, octal and hexadecimal number systems to decimal number system. So I hope you have understood whatever I have explained in this video. If you have any query or doubt, you can connect with me by following these details. Thank you for watching this video. Keep following my YouTube channel. Thank you.