Number Bases Made Easy | Complete Mathematics Revision for WAEC, NECO, JAMB & Post-UTME (LIVE)

[00:00:29]So welcome to easy science TV. I'm sure you can hear me clearly.

[00:00:36]Thank you very much. Now we are going to be looking at this the topic. So let's look at number bases.

[00:00:46]We looking at number basis and all the questions under number basis. So we are going to be looking at them one after the other as we prepare for as we prepare for jump next year and why this year. So let's gradually um look at all the questions on number basis. So these are very popular topics and we have to deal with it but if we don't deal with it the topics will keep being an issue to most students. So this is the question. So welcome to science TV. I appreciate all of you for always participating in our live streams and videos. So I appreciate a lot. Now we have a question on number basis and we are going to expand it. Remember what I said initially. So in my previous live stream we most of our viewers actually testify that they did so well. So I know that those of you that are watching us after watching us you are actually going to do extremely well if you follow the instructions we give in this channel.

[00:02:03]Now let's proceed without wasting much of our of our time. So we are going to expand by using this is one okay this is 1 * x remember what I said this will be 1 * x then plus this is 0 * x okay 0 * x and this is 1 * x as well okay this is another one * X and this is equals to 5.

[00:02:45]Now I know you may want to ask me some questions. Always expand this way first.

[00:02:53]This is the first step in case you can hear the sound of rain. Okay, please. I hope it's not obstructing the sound.

[00:03:02]Okay, if it's not obstructing the sound, let me know in the chat section. Okay, just let me know. I just want to be sure.

[00:03:11]Now, the reason why I have to meet this one here, the zeros, this second position, because this is zero, whatever we get at this point. When you multiply by zero is going to give zero. So, this point here is meaningless. So, neglect this point. That's why we have done it this way. Then don't forget at this point at this position here x will be powered by zero. So which means we are going to have zero here.

[00:03:45]Then at this other point here x will be powered by this is 0 1 2. We are going to have two right here.

[00:03:57]Okay. This is one. Here is supposed to be one. So we are supposed to have 0 1 and two.

[00:04:07]But note that at this point there is zero which means that position to us in expansion is meaningless simply because whatever you multiply by zero will be zero. So there's no point wasting our time. What we are simply going to do is to work with these ones. So let's proceed.

[00:04:32]1 * x² will give us x² then plus.

[00:04:42]So 1 * x² will give us x² then plus 1 * this. Okay. 1 * 1 x is raised to power 0. Whatever we raise to the power 0 according to the law of indices is going to be one. No matter what it is, whether it is symbol, numbers, no matter the magnitude, we are always going to get zero when it is lifted. When it's lifted to zero or power by zero, we always get one. So that is how simple that is. and this equals 5.

[00:05:24]Then x² + 1 * 1 is 1 and this is equ= to 5.

[00:05:36]So we can transfer + one to the right hand side. We'll now be left with x² at the left hand side. So x² = 5 + 1 when it is moving the other way becomes + 1. This is what is going to be. Then we can go ahead and subtract.

[00:05:59]This gives us x² is equ= to 5 - 1 is 4.

[00:06:08]Once you are done with this, we go ahead. Let's get the square root. Right?

[00:06:13]Take the square root of both sides. So let's take the square root of both sides. If we take the square root of both sides, it means we are going to have x. The square root will cancel this square leaving us with x. Okay, we are going to be left with x.

[00:06:33]So this will give us x as 2. This is the solution to the question. There is no other thing. Okay? No worries, nothing at all. Which means x is equals to 2.

[00:06:48]That means that this number is a base 2 number. So I hope this is well understood. For those of us that are just joining, I do hope we'll understand what is going on here. So we just started this and uh if you are joining us and you are not subscribed, please do well to smash the subscribe button because a lot is about to be given out.

[00:07:09]Don't forget our revision series comes up around August. So we are starting revision we are starting our lectures and lessons and tutorials towards JAM and GC and SAT as well as every other exams that will come up in the next 6 months to one year. So do well to subscribe so that you don't miss our lessons, videos and shots. So this is how we are going to begin. Welcome to AS Science TV. If this is what you love and you want others to have it, why not go ahead and share it? Do well to also like this uh live stream so that YouTube will keep promoting it to a lot of other persons. Now, let's proceed to the next question. It is the same thing. Let's look at what we have right now. Right about now. Okay, this is another question. This is another question.

[00:08:01]Let's look at this question. Very interesting question.

[00:08:12]So the topic is number basis. Okay. It can involve equations in number bases and it can come in different forms. All right. In different in diverse forms.

[00:08:25]Yes. Look at this one. This is one P 03. Yes. 1 P3. We are going to look at look at this particular one is one uh 0 0 okay one right then is still in base two H it's still in base two then this is equals to okay let's change this for instance let's change it to base 10 H let's change this to B 10 what is it going to be so who can give us the solution to In base 10, what is it going to be?

[00:09:07]Remember, we just want to expand it. So, if we expanding, this will be zero. This will be one, this will be two, and this will be three. This is how simple it is.

[00:09:18]All right? There's nothing to worry about this at all. So, this is one.

[00:09:24]Remember I said this is one * 2 plus another 1 * 2. This is what we are going to have.

[00:09:35]Okay. 1 * 2 and another 1 * 2. No matter how many the zeros are, no matter how much the zeros are, how many are there is not important. Just focus on this one and this one. This is zero and this is three. Remember that. Very important. So at this point two, we carrying zero when multiplying one. So that's this point here. Which means we are going to fix one here. It has two^ Z.

[00:10:07]Then at this other point two will be carrying three. We're multiplying one here. So which means you're going to have three.

[00:10:17]So we are converting from B 2 to B 10 using the expansion method. There are different methods but this is the expansion method. Okay, that's what I'm showing you here. Now the next phase is for us to simplify or evaluate the numbers. This gives 1 * this is 2^ 3.

[00:10:38]What is 2^ 3? Remember 2^ 3 is equ= to 2 * 2 * 2. And the answer to this is 3.

[00:10:50]2 * 2 * 2. The answer is what? 8. Do you get it now? This is eight. So which means you're going to add eight here because two is multiplying itself three times. So the answer is 8. 2 * 2 is 4 * 2 that's 8. We are going to let this go.

[00:11:11]Then this is + 1 * 2^ 0. Whatever to the power of 0 will be one. So we are going to write one here.

[00:11:27]Then go ahead. 1 * 8 is 8. Then plus 1 * 1 is 1. Which means our final answer is 9 and this is in base 10.

[00:11:43]Always note that this this is base 10.

[00:11:45]This is in base two but we converted it to base 10.

[00:11:49]Okay. So that is how to solve this kind of problem. All right, take note of that please. Now let's look at the next question. This other question.

[00:12:01]Yes, very interesting question. Very funny as well. So we have to look at this question. Look at this question.

[00:12:07]Let's evaluate this other one. In this case, we are evaluating like number one. So we are in number three. Now in number three we have to find x. Find x if we have to find x.

[00:12:29]Find x if 1 0 1 1 0 1 1.

[00:12:44]Yes. 1 0 1 1 base 2 + x 7 Okay, base 2 + x B7 is equals to 25= to 25. This is what we have. I'm sure we can see everything. Hope the camera captures everything. If you can see, let me know in the comment section or in the chat box. I just want to know. Okay. So, I do hope we are all seeing it, right?

[00:13:21]If you can see it. Yes, we are all seeing what we have on the board. So, that is the application. Now, what we are going to do is to expand this one.

[00:13:33]Then simplify this and work it out together. So, let's begin with this. In this case, we have 1 * 2. Okay, that is 1. Remember I told us we have 1 * 2 plus this is zero. We don't need it. Neglect this zero. Neglect this one. Go to this one. The second one that's 1 * 2. Then plus the last one here, which is also 1 * 2. You can see it. We have expanded this, right? So here will now be zero.

[00:14:07]From here this is one. So two will be having one. This is 0 1 2 3. So the last one here will now be three. Then we can add we can do that of seven x. This is 7. Okay. 7 x raised by what?

[00:14:31]Remember this is seven. Okay. Okay, let me let's do it the way we did this so that you understand better because this is going to be x * 7 just like we have 1* so this will be x * 7^0 and is equals to 25 the 25 is is in base 10 please take note the 25 is in base 10 so let's put base 10 here but here no need for the base 10 so we are going to expand Understand this or evaluate this 2^ 3 we are already aware is 8. So we're going to write 8 here plus 1 * 2.

[00:15:15]Okay we have 2^ 1 is 1 is two rather then this other one is 1 * 1. Remember I told us that whatever we raise to the power of zero will give us one. No matter what it is then 7^ 0 is 1. That's x * 1 = 25 = 25. That's what this is. Remember where you have zeros whatever if 0 is the power it will always change to one.

[00:15:53]Remember this. These are basic things in binary numbers or binary expansion. So 1 * 8 is simply 8 plus 1 * 2 is also here as 2. Then + 1 * 1 is 1.

[00:16:13]Then plus x * 1 is x.

[00:16:21]And this is equals to 25.

[00:16:26]This is equals to what? 25.

[00:16:30]So we can add up these ones, right?

[00:16:33]Let's add it up. It's 8 + 2 that is 10.

[00:16:38]8 + 2 is 10 and + 1 that is 11.

[00:16:43]That is 11. Sorry for the noise. this 11 + x is equals to 25.

[00:16:57]Okay, when you add up everything here is 11, then this is 25. Then we can simply shift or take 11 to the other side. If we do that, we are going to have our x left here at the left hand side. Then at the right hand side we have 25 - 11.

[00:17:20]Then x is simply going to be 25 - 11.

[00:17:27]Just reduce each of them by one. This is two becomes one. This is five becomes four. So that is 14. That is what it means. Okay. That's 14. So x is 14.

[00:17:41]Remember we have it in B7 but doesn't that's not the issue here. The fact is that X is 14. That is exactly what the answer is. I do hope you are getting value in this video. Don't forget to smash the subscribe button if you haven't. Okay, because with that the channel will keep growing. Thank you for joining this channel. I appreciate you a lot. I think most of our jam candidates actually gave positive testimonies as to what they benefited from AZ Science TV because this channel actually gave them an edge when they got to the submission hall. It was very easy for them. There was no issue at all when they got to the exam hall. So please do to smash subscribe button and turn on the notification so that YouTube will always notify you whenever we are on live in this channel or whenever we turn in videos and shorts. All right. So watch our videos you will see that you have a lot to gain. So that button is waiting for you to smash it. It's begging you.

[00:18:42]Please do that now. Thank you very much.

[00:18:45]So let's proceed. Um here we have to find x here. Okay, remember we're using the expansion method. These are equations equations involving um number bases. So these are number bases. You can see them base 2, base 7 and base 10. The bases are not the same.

[00:19:06]We have to look for a way to unify the bases. Make the bases to be the same.

[00:19:11]This is two. This is seven. And this is 10. So we decided to make all of them 10. 10 10. By expansion, we have made here 10. By expansion, we have made this one 10 in here. And by expansion, this one does not need to be expanded because it's already 10. Now, since they are the same, we can go ahead and simplify them in base 10 and that gives x to be 14.

[00:19:37]And that is the solution to the question. Thank you very much for watching. We are simply going to move to the next one without wasting much time.

[00:19:47]We are not going to waste any time at all. Okay. So this is what we are going to do. We are going to we going straight to the next one. Yes. Let's look at this one which is quite uh easy, straightforward and without any stress at all. So let's look at this particular one. Very easy. Okay, very very easy. So we are given that if if if one if 1 P 03 if 1 P 03 in base 4 in base 4 is equals to 115 is equals 115 in base 10.

[00:20:47]Now the question is that we should find P.

[00:20:53]Find P. This is the question. We have to find P. This is one. This is zero. This is three. Please take note. Neglect this zero. As I earlier said, okay, the only unknown here is P. So don't worry yourself when you find something like this. Now let's look at the solution or the answer. So the solution is this.

[00:21:14]Let's call it solution. Okay. So we have one, we have P, we have zero and we have three to the base of four. And all of them equal to base 10.

[00:21:39]So we are going to expand the way we did the previous one. This is 1 * 4.

[00:21:45]Remember call it 1 * 4 just plus. Okay.

[00:21:50]This is P * 4. So just let it be P * 4 then plus. This is 0 * 4. No need for this. Please always neglect the zeros to make it faster. Especially in exam hall, if the zeros are five, just abandon the five zeros and focus on the nonzero digits of the number base of the numbers. So this is zero. Forget it. Go to three. We are immediately going to look at 3 * 4. Then this is equals to 115.

[00:22:29]Neglect the 10. There's no need for the 10.

[00:22:32]Okay, because we know that it's already in base 10. Whenever there's nothing here, just know that the number is in base 10. So, we proceed. This is 0 1 2 3. So, at this point, four will be carrying zero. Then at this point, this 0 1 2. Okay. Four will be carrying what? Two.

[00:23:00]Two. Then at this other point four will be carrying three. It is 0 1 2 3.

[00:23:09]Now we are going to expand. Okay. We going to expand as quickly as possible.

[00:23:16]So let's use the available means here which is our calculator. We using our phone as calculator. So we use our calculator in the phone. So here we're going to write 4 * 4 * 4. Okay, that's 1 * so 4 * 4 * 4 is 4 * 4 is 16 * 4 okay that is 64 that is 64 plus this is p which is the unknown * 4² is 16 okay then this is going to be 3 * 1. I'm sure you know why it is one, right? It is simply one because 4 is power 0. So whatever power 0 is one and this to 100 that's what we have right here. So 1 * 64 is 64 + 16 p.

[00:24:35]16 p + 3 + 3 = 11 15. Now we are going to add up these two because they are alike, right? So 64 + 3 is 67. So that gives 67 + 16 P is equals to 100 and 155.

[00:25:08]So take 67 to the right hand side.

[00:25:12]That's leaves us with 16 P. So we are now left with 16 P.

[00:25:18]16 P is equals to 115.

[00:25:23]115 minus this number here 67us 67.

[00:25:32]So we can do the subtraction 115 - 675 - 67. So we have 48.

[00:25:44]So it means that 16 P 16 P which is what we have here equals 48.

[00:25:55]Once we have this the next thing is for us to divide Divide by 16 at the left hand side by 16 at the right hand side.

[00:26:07]So what would be the value of P? It is quite obvious. We now know what the value of P will be right. So it's obvious that P P will be equals to 3. Okay. P is equals to 3.

[00:26:28]That is implication. So P here will be equals to 3. H one way to test if you are correct. You can there's no point if you can substitute here and get 115. But in a quick way to know if we are correct or not, none of these digits should be equal to none of them should be equal to or greater than four.

[00:26:51]Okay, you can see this is 10. So none of this is up to 10. This is four. No number here, no digit here should be up to four. If if you got any number that is up to four or greater than four, it means that we are not correct. Then we can check the errors and see how we can amend our mistakes or amend our answers.

[00:27:14]I hope this is very very clear and uh correct right. So any question if you have any question let me know you put it there I will answer the question as quickly as possible right so I am waiting for your question do you have a question there let's let's see in the chat box I will soon be there I'll check the chat box to be sure that we are okay so let me check the chat box let me check I've not checked in a long H.

[00:27:49]So any question? Nobody's talking to me.

[00:27:54]Come on. Please let's talk to each other. Okay. Let's communicate with each other. So I'm going straight to the next question. Please permit me to rob the board. I have another question here that we have to solve as quickly as possible.

[00:28:13]Yes, we are going to solve a question now. very interesting one. I hope we are following especially my students that are preparing for examinations.

[00:28:25]Okay. Post students, uh, next year's jam student. Yes. And GCA students. Now we are to find the value of M. Okay. Find the value of M. This is another question. Please permit me to write it.

[00:28:42]Find the value.

[00:28:45]Find the value of m if if yes we have to find the value of m if 13 m if 13 to the base of m + 24 to the base of m + 24 to the base of m is equals to 41. 1 to the base of m is equals to 41 to the base of m.

[00:29:22]I'm sure you can see this question, right? So, how do you handle this question? Yes. Who can tell us how we handle the question? H the questions this question is very easy because the base are the same, right? Yes. That's what somebody's going to say. The base are the same. But we are going to expand all of them. H expand them to base 10.

[00:29:45]Okay, we know you see that this is an unknown base. So let's quickly do that without wasting much time. This is going to give us let's write a solution here. So we have 13 m right that is 13 to the base of m + 24. This is not 13 m.

[00:30:07]It's 13 to the base of M. And this is equals to 41 to the base of M. Please take note. This is very important. So let's expand. This is 1 * m. Remember what I told us 1 * m.

[00:30:26]Then plus this is 3 * m. Just write it.

[00:30:30]Forget about the power. Okay?

[00:30:34]Don't bother about the powers. Just expand like this and leave it first. But don't forget to come back. You must come back and complete it. This is two, right? That is 2 * the base which is m.

[00:30:50]Then plus this is four. That is four * m. We're not done yet. We are still going to handle the other one. This is four. Okay. This is 41, right? Which is four, not 41. It's 4 * m + 1 * m. I'm sure we can see. You can see this. Okay.

[00:31:16]Now we proceed. Look at this. Don't forget this is 0 and one. Zero on top of three here and one here. So which means m will be giving zero here and here m will be given one.

[00:31:33]At this point which is this one is 0 and one too. So m will be given zero here.

[00:31:41]Y here m will be given one. What about this point? Same applies to all of them.

[00:31:48]Okay. M will be given zero here. Then m will be given one right here. So we can go ahead and evaluate it. 1 * m^ 1.

[00:31:59]Right? Okay. Let's write 1 * m.

[00:32:04]This is 1 * m plus this is 3 m^ 0. Anything raised to the power 0 is one. Doesn't matter whether it's a number that is power 0, it will be 1. If it's a symbol like alpha^ 0 is one. If it's a letter m k z^ 0 is one. So this is going to be * 1.

[00:32:34]Take note please. Then let's proceed.

[00:32:36]This is 2 * m. This is 2 * this is m^ 1.

[00:32:42]That's m. Then at this point we have the same thing 4 * 1. I've explained already.

[00:32:51]Then we have 4 * m + 1 * 1. I'm sure of know we have one here and * m^ 0 which is 1 here. So 1 * m is m. We are going to write m + 3 * 1 is 3. So we write 3 here + 2 * m is 2 m. Please 2 m. Note that then 4 * 1 4 * 1 is simply four.

[00:33:34]Then to the right hand side we have 4 * m. Please this is m don't forget it's not a symbol. 4 * m is 4 m. Not this. So please this plus 1 * 1 is 1.

[00:33:55]This is what we have at the right hand side and this is the left hand side. We can go ahead and simplify them. Let's bring like terms together without wasting our time. This is m. Let m remain where m will be. Where will m be?

[00:34:09]Let's transfer all the m to one side and all the numbers to the other side. Okay.

[00:34:14]So this is 4 m. Bring all the m the other way and take all the numbers or constants to this other way. So this is three. We are going to write three here.

[00:34:25]Plus this is four. We write four. This is + one. Bring it to the left hand side becomes -1.

[00:34:36]Then equals to we are left with 4 m at the right hand side. So leave it there.

[00:34:44]Then we have m here.

[00:34:47]Bring it. Remember m means 1 m. So when it's crossing changes to minus1 m + 2 m becomes - 2 m. If you check we have 1 2 3 4 5 6 that's 1 2 3 4 5 6. So nothing has been omitted or neglected. So 3 + 7 3 + 4 is 7. Okay. And 7 - 1 is 6. So which means we have six here at the left hand side.

[00:35:24]Then at the right hand side 4 m - m - 2 m will give us remember we have 4 m.

[00:35:35]This is - right? That's - 3 m.

[00:35:40]That's what it is. So that gives 6 = m.

[00:35:46]Therefore, m is = to 6. That's what it is here. So, m= to 6 because 4 m - 3 m is 1 m or m.

[00:36:00]Okay, that's what it is. So, I hope this is well understood. I'm trying as much as possible to break it down for proper understanding. Okay, I hope you are following. If you are not following, let me know in the chat box. Please talk to me. Okay. And if you have not subscribed and you're watching, you are coming um to science TV for the first time and you have not subscribed, please go ahead, hit the subscribe button, okay? The button is praying for you to hit it.

[00:36:29]Please do work to smash that button.

[00:36:30]It's very important cuz it keeps the channel running and running. Okay, thank you for joining Science TV. So we are going to move straight away to another very crucial and very popular why question on number basis. Yes, these questions are always very popular. You always find them in number basis. Yes, in questions. So let's look at them. For those of us that are writing post and so on, note these questions are very important. Yes, check the past questions. You will see them they are always there always. So please it may come in different forms but the basis is that they are there. Yes. So let's look at it.

[00:37:22]Let's look at this other question. This is coming in three folds.

[00:37:27]in three fours add. This is simply addition. Look at this addition. Add add 1 1 0 1 1 0 1 in base 2.

[00:37:47]Then 1 0 triple 1.

[00:37:50]1 0 1 1 in base two. and triple one and one one one in base two. We are adding these numbers together. Some students will be wasting their time. We don't waste time. Whether it is plus plus and minus or plus or plus and plus any one you find just go ahead and solve it.

[00:38:21]Don't waste time. Don't waste time. This is what to do.

[00:38:26]Just go ahead and arrange it like this.

[00:38:30]Look at what I'm going to do. This is 1 2 3 4. So this is one. So let me put zero here and put one here. Okay, this is what we're going to do. Then for the second one, remember this is the biggest one. We may decide to start with the biggest one if we choose to. We'll start with this one which is the biggest. All right. So let's let's even not bother.

[00:38:53]Don't worry. Okay. Since we have 1 2 3 4 5 we can we can make it yeah we can make it to be what? Zero. So 1 2 3 4 5. This one was not included initially. What we have is this. But because we have five digit here to balance the four digits and three digits we include zero here.

[00:39:18]Then the second one we now start from here. Then this is zero. This is one one and one. Remember it's addition.

[00:39:30]Then the third one is from here, right? So this gives us what? H one, one, one. So we have one, one and one.

[00:39:43]You can see it. So that's what we have here. Then we are going to simply add together. There's no big deal. This is plus. So we adding let the addition be here or somewhere close here then we can go ahead and noting the base please base the base is in is two yes that is in base two just add up 1 + 1 is two and plus this one that is three okay but we're not going to write three here we're not writing three instead of writing three here we are simply going to write three which This is the three we got here divided by this two. So we are going to divide by two that is under this point here divide by two. If we divide by two two will go into three once.

[00:40:38]This is not what you going to write.

[00:40:40]Please take note of this. Don't write this one. The number of times that two goes into three. Don't write it. This is what you're going to carry to the second column. To the next column. This one.

[00:40:52]The number of times that two goes into three. Carry it to the next column. Then the remainder write it here. What will remain? Remainder is one. So this remainder, this remainder, write it here.

[00:41:07]Please take note. This is not this one that you are bringing here. It is this other one. They are not the same because the position differs. So please take note. Then this other one that is left here, come and put it at the second or at the next column. Then add it again.

[00:41:25]If you add it together, 1 + 1 + 1 will give us three again. So we going to write three again here. Then divide it by this two. If you divide by two, what are we going to get? Still the same, right? We are going to have one remainder one. Okay, one remainder one.

[00:41:49]Then this one, come and write it here.

[00:41:53]This is where you're going to write the one, not the three. Okay, then this other one, transfer it to the next column. Where is the next column? This column. Yes, this is the column. You see it now? Transfer it to this column.

[00:42:07]becomes 1 + 1 which is 2 + 1 3 another one that is 4. We are now going to write four four we are not writing the four inside here because four is not the answer. Divide by base 2ide by this base 2. So what are we going to get here? 2 into 4 is two. We are not writing this two here. You see why I'm saying we are not writing this first number here. So this is two. Don't come here and write two. Please it is wrong. It's wrong.

[00:42:44]Please don't write two there. Okay. What you are going to write here is the remainder. Always write the remainder.

[00:42:50]Okay. Just like modular arithmetic also.

[00:42:53]This is two. Remainder.

[00:42:55]Remainder what? Zero.

[00:42:58]Remainder zero. So this zero this zero here. Come and write it under this column. under this column. Then the next one is this.

[00:43:09]This is what we are going to carry.

[00:43:11]Carry this two. Bring it to this point here. Then add it.

[00:43:18]When you add 2 + 1, that is three. This is zero, which is meaningless, right? So it's three. We are now going to write three again. Under this column, we write three. Remember, you can write zero and zero here. And just like I told you to balance up the number of digits just write 0 0 since there are only three digits here. So once you have added and you have gotten three divide by two just like what we got here that's what you are still going to get here. So your answer is definitely going to be one here. Look at there one one where you get 3 three you will get one. Yes. There is no argument about that. Okay. Don't worry yourself about that. There's no worry at all. We going to get one. But what will remain is one. So it means we we wrote one and remain one. So this cement one is what is here. Then this other one carry it. Carry this one. This is called carry. C for carry. Okay.

[00:44:17]Carry. Carry this one. Carry this one.

[00:44:19]Carry. Carry. Carry. Carry. Okay. Carry this one. Drop this one here. H. Okay.

[00:44:29]So if you carry this one, put it here.

[00:44:32]Add up 1 + 1 that is two. Good. Don't write the two here please. No number here must be equal to this base. So we are going to write the two here under this column please. If the column is you can adjust it so I can have a column H.

[00:44:51]Then divide by this two. If you divide by this two, we are going to have one remainder zero. So this zero here, come and write it here. H it is this zero that you are going to write here. Then we left with one. If you put the one here, there's nothing to add it to, right? So that's why we are simply going to put it here. H or if you like come and put it somewhere around here, but it won't make sense because it will look like it is one of these digits. No, we don't want it to be like that. they just come and write write it here. This is the simple way to solve this. I know a lot of students might be finding addition, subtraction and even multiplication and division of bases. In our subsequent classes, we're going to deal with other other ways to evaluate bases. Both the addition and subtraction we have done the addition. Now you see how simple it is. So just know how to carry, which to carry, which to drop.

[00:45:50]Okay, this one is drop. Drop this. Carry this. Drop this. Carry this. Drop the remainders. Carry the number of times.

[00:45:59]It's the coefficient. Okay. Yes. Just carry the quote. Drop the remainder.

[00:46:05]That is how to solve this. And the solution to this is that when you add these three binary numbers, you are going to get this in base two. That is base two. Please. This is in base two.

[00:46:19]Let me write it in words.

[00:46:23]This is exactly what it is. I hope it is well taken and well understood. And I do hope you're getting value in this video.

[00:46:30]If you're not watching, if you're watching this content and you are not a subscriber yet, what are we waiting for?

[00:46:36]Go ahead now. Come on. Okay. Smash that button. Smash it. It's waiting for you to smash it. Okay. That is why we are here to work together for the good of one another. Okay. Just like we are here together to push forward. So this is exactly what this question is. We are simply going to move on to the next one.

[00:46:56]But before then let me check the the platform to see how engaging are we okay. Is there anybody? Okay. Nobody is commenting. Nobody is saying anything.

[00:47:09]Why are we so quiet? I hope we are okay.

[00:47:12]Are we fine? All right. I know it's weekend so a lot of people are so relaxed and and they want to have their weekend to themselves just like I'm taking your weekend please I'm going to let this go so that we can take the next one. Now we have another question this is on subtraction of of number basis or let me quickly solve this one. Okay let's look at this subtraction first then we solve. So we have done addition.

[00:47:42]We are now going to look at subtraction.

[00:47:45]Let's look at the subtraction and see.

[00:47:47]Look at this subtraction. Subtract.

[00:47:51]Yes, we have to subtract.

[00:47:54]Look at this.

[00:47:56]Yes. Sub um 16 418. Subtract 1 6 4 1 18 in base 9 in base 9. Yes. From 18 630.

[00:48:16]From from 188 6 in base 9. Yes, both of them are in base 9. So we are going to subtract this from this.

[00:48:34]Remember we have done addition. This is subtraction.

[00:48:38]So let's look at subtraction.

[00:48:43]So we are going to arrange it. Let's arrange which one is greater. This is 18. This 18 is 13. This is 16 41. So and they are the same digit which means 18 is greater. We are now going to subtract 1 8 6 30. Then this other one is what?

[00:49:04]Remember always start from here except they are of the same number of digits.

[00:49:09]So here we have 1 6 4 1 and 8. Remember it is in base 9 and we are subtracting which means we have minus here and the final answer will be here. Usually this kind of question don't have much issues. Addition always increase numbers but subtraction reduce them. So whenever you are subtracting this is in B 9 the numbers the final numbers are usually less than the base.

[00:49:43]So those divide by this, drop this, carry this, they are usually not there.

[00:49:48]So let's proceed. This is zero.

[00:49:52]Whenever you find zero, remember the base is nine. We are going to borrow from one here. We borrow one from three because it is impossible to subtract eight from zero. So borrow borrow one from here. That one becomes 9 because we are dealing with base 9. So this becomes 9. Okay. Longer this one.

[00:50:19]We are no longer going to use this. We use 9. We are now using 9 in place of zero. So 9 - 8 is simply one.

[00:50:29]You see how simple it is, right? What are we left with here? This is already gone. We are now left with two. So put the two there. Okay. and circle. This is this is two. The ones we are going to deal with, we're no longer dealing with three. We are dealing with two. Three and zero are gone. It's now 2 and 9.

[00:50:51]Okay. 2 - 1 is simply 1. This is how simple it is. Okay? We have not removed anything from 6. So 6 - 4 is simply 2.

[00:51:04]Remember, we are not dividing by 9.

[00:51:06]Carry 9. Drop 9. Carry this. Drop this.

[00:51:10]simply because none of these numbers are up to 9. If any of them was to be up to 9, we would have divided by 9. And write the remainder. Drop the remainder. Carry the coefficient. Okay. Now this is 8 - 6. 8 - 6 is also 2. Then 1 - 1 is nothing. So you decide to leave it there. Okay? Or you put zero. Usually we don't write it. But if you want us to write it for better understanding, write it. So the final answer is 2211 in B 9. Please never pronounce this one as 2,00 you know 2,211.

[00:51:56]No, because this is not B 10. Okay?

[00:51:59]Instead of saying 2,00 say because the the multiples here the base is 9. So it must be pronounced with respect to 9.

[00:52:08]not with respect to t unit thousands those units are those uh those ones are for base 10 please take note this is how to handle this kind of question now we are going to go back to equation let's solve one more equation okay but I'm going to t let's solve together as we as we handle that equation so I do hope this is well understood this is quite easier so subtraction is quite easier compared to uh to the other ones. Okay?

[00:52:41]Cuz subtraction we we decrease the numbers. The number was formerly 18 18 630. That's sorry I'm sorry for calling it 18. It's not 18. Please 18630.

[00:52:53]But now it is 022 1. So there's a decrease. That's why it's very easy. Now let's proceed to the other one. The next one. Okay. Here we are to um we are given that if 55 if 55 to the base of x to the base of x + 52 + 52 to the base of x is equals to if this is equals to 77 77 to the base of 10. Now the question demands that we find x.

[00:53:48]Find x that is find the value of x. So who can help us with this? I'm sure someone has the solution to this question. So let's proceed and see. Yes.

[00:54:02]Before we get to the end of this question, I want you to drop the answer if you know the answer. Okay? I'm sure someone watching me right now have the solution. So, I'm waiting for your answer. Once I finish writing solution, I'll come and take solution from you because I know you have the solution.

[00:54:19]All right. Yes. So, we are simply going to expand. I'm using expansion method because that's the that's the direct method for this. We can't using the repeated multiplication method. That is not very good for this kind of question.

[00:54:35]Okay. So remember what we have here. We have 5x.

[00:54:41]So we have 55 to the base of x. Please this is not 55x. This is 55 to the base. Sorry to the base of x. Then this is 52.

[00:54:54]52 to the base of x as in to the base of x equals to 77 h to the base of 10. Can see it. So let's expand this is 5 * x. Remember that's how we going to write it. 5 * x then plus this is 5 * x.

[00:55:19]Again we are going to repeat the same thing here. Write the same thing. 5 * x here. Then this is what?

[00:55:29]Don't worry about the powers. Okay.

[00:55:31]Don't worry about the exponents. Let's just proceed and expand everything. Then we can come back and fix the exponent.

[00:55:37]But you know you're going to forget. You can go ahead and do that. Okay. But it's easier to just move this way. Now this is five times this x again. Then plus we have 2 * x 2 * x. We are now going to equate it to 77. And when doing that, neglect the 10 because 77 is the same thing as 77 b 10. There's no need to bring in the 10 again. So 5 * x is 5 x then plus 5 * x again is another 5 x okay that's another 5x then plus okay uh yes plus we are still moving take note 5 * x this is another 5x 5x right mhm okay So I'm sure we are already that's what I said initially that we might forget it but I would have used that method h remember remember this point here this is zero this is one this is zero and this is one okay yes this is zero so x we have zero here then x will have zero here and x will have one and one here please take note So let's pinch zero on x here. Then we pinch one on x here. That is the exponent. These are the exponent of x. We're multiplying five and five. Do same to this place.

[00:57:24]This point here. Pinch zero here as the exponent. Then pinch zero here as exponent. So we can now go ahead. Right?

[00:57:35]This gives us 5 * x plus here it's no longer 5 * x that that's to tell you that zero is very powerful. So don't joke with zero. So zero can reduce anything right. So this gives five * 1 5 * 1 then plus this is 5 * x look at it here from here they are the same so this is 5 x then plus this other one is the same which is you can see it okay so this will now be 2 * 1 whenever it is 3 to^ 0 just have it like this and this gives us 77 this gives 77.

[00:58:36]So 5 * x is 5 x is 5 x then plus 5 * 1 is 5.

[00:58:53]Okay. Then 5 * x is still 5 x.

[00:59:00]5 x then plus 2 * 1. Okay, 2 * this one here is simply two.

[00:59:10]Then we can simply equate everything to 77.

[00:59:16]So just collect the terms that are like bring similar terms together, transfer the other terms that way. So here we have the terms in x 5x and 5x. So bring it together that is 5x and 5x here added together equals to this is 77.

[00:59:38]So have it at the right hand side.

[00:59:41]Transfer these ones to the right hand side that is -5 and this is + 2 becomes minus2 when it crosses to the right hand side. So first before you continue always double check.

[00:59:58]Okay, just like before you transfer money from one bank to another, you double check. So let's double check. If you count, you see that we have 1 2 3 4 5. So count the number here. Okay, the number of terms both the constant and so on. If it's up to the one we have here, then you are correct. That's 1 2 3 4 5.

[01:00:20]So we are okay. Then we can proceed. 5x + 5 x is simply 10 x and this is equals to so we can proceed remember this is 77 - 5 is 72 and 72 - 2 is 70 that gives here to be 70 now that we have gotten this we are looking for the value of x find x That gives division. We divide by 10 on of the sides.

[01:00:58]If we divide by 10 on each of these sides, it means that this will go leaving us with x will be equals to 70 / 10 is 7.

[01:01:14]So this is quite straightforward, easy, easy, very simple, right? Like a piece of cake. So that is how to solve this kind of questions. I do hope we are getting values for this um live stream.

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[01:03:08]Okay? So that if you didn't get it now, you can go over it when it is in when it has been uploaded again after this live stream. Thank you very much for watching. I'll see you in my next lessons and live streams. Uh for now I I wish you goodbye and I wish you excellence in all your examinations.

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[01:03:33]For now, goodbye and enjoy your weekend.