A Binary Lesson
Thanks to the advice of my guidance councilor, I have taken one of Professor Harpers introductory mathematics classes. It's not just about the normal problem solving you get from most math classes, but it's supposed to give us a deeper understanding of how numbers work and are used in various fields. That way we can better choose which fields of mathematics are best for us to follow based on our other needs and majors. The first few weeks have just been overviews of what we are going to cover throughout the semester, but now we are about to start our first segment, which is about computers and how they run on math.
In our last class before the weekend Professor Harper said that he wants all the girls to be involved in an example up in front of the class on Monday, so he asked them all to wear longer than usual skits or dresses and not come to class without them. He seemed to think this was a very important point and said that any girls that showed up bottomless would be marked down for it. I figured he didn't want us being distractions while he was trying to give his demonstration, which I can understand. Some of the girls in the class can be quire distracting, especially when they show up bottomless or in their tiny little skirts.
So when Monday morning came around I dressed in the light and floaty, pale blue, spaghetti-strap dress we had picked out on Saturday. It came down to my knees, which seemed more than long enough for what the professor asked us to do, but still looked really nice. I just had to make sure I kept it on at least until his class that afternoon. So I made sure I was only wearing the dress and had nothing else on me that could possibly be mistaken for clothing. I didn't want to end up getting inspected and having it all confiscated.
It was a good thing I did that too. It seems that wearing a knee-length skirt was pretty much asking to be inspected. The first time I was stopped was on my way to my first class. I had to go through the whole thing, following instructions to the letter to make sure it went smoothly, and then getting my notice saying I was clean, finally allowing me to put my dress back on. I was then stopped no less than three more times throughout the day, but I just had to show them my inspection slip and they let me go on my way quickly.
Finally I made it to my math class and was still wearing my dress, so that was good. As I walked in and took my seat I saw a couple of the other girls who had arrived before me. Each of them seemed to have about the same idea I did, being dressed in skirts and dresses that were about knee-length. I even saw an inspection slip sticking out of one of their math books like a bookmark. I had a feeling we would all have similar stories to share if we asked, but instead I simply sat down and waited for class to start.
As the start time grows closer other students start to shuffle in and I catch sight of a couple girls walking in naked and looking worried. Both of them seem to be clutching inspection notices. Fairly soon everyone appears to be in attendance and the professor walks in, closing the door behind him.
"Good afternoon guys." He said, approaching his desk.
Most of us mumble a reply, but nowhere near in unison. "Good afternoon Professor Harper."
He drops his case on the desk and turns to look at the class. "I see some of you did not heed my warnings. I hope we still have enough to do this lesson."
He then pulls his desk backwards against the wall, clearing a large spot on the floor in front of the class. "Alright, Penelope, Laura, come up here and explain yourselves."
Penelope, a curvy brunet with huge tits, rises first and walks forward with her hand outstretched. He looks down at the slip of paper in her hand, but doesn't reach for it. She shakes the hand, trying to get him to take it and says, "I was inspected and they confiscated my dress. It's not my fault."
"Not your fault?" He asks, looking skeptical.
"No," she says, almost whining. "They took my skirt. I don't have a choice in that. You know how inspections work."
"That's right," he says, "I do know. And I know that if you had no violations and followed instructions you would have been given back your dress when it was done. Somehow it seems like it has to be your fault, otherwise you'd be here in your skirt or dress."
She looks like she is about to argue, but then just lowers her head, giving up. I almost feel sorry for her, but he has a point. I was inspected and I still have mine.
Laura, having seen this happen, crumples up the slip in her hand and palms it before the professor can notice it. He turns to look at her and says, "How about you? What's your excuse?"
She simply lowers her head and says, "Sorry professor."
"Well," He says, "The two of you are in trouble and will earn no points for today's lesson, but you should still stick around and learn something. It will be on the test. You're lucky there's enough that did do as I asked to allow us to continue. Now go take your seats."
The two naked girls, with their heads still bowed, turned and walked back to their seats. Professor Harper walks over to the side of the room, leaving the large floor space in front empty, and turns to look at the rest of us. The tension in the room is palpable as we all look at him and wait to see what this special lesson is about.
"So you all know how to represent numbers using the standard symbols we use, called Arabic Numerals. What most don't know is that the actual system we use is called Base-10 or the Decimal Number System. That means there are only 10 symbols needed to represent all numbers that can be formed. These ten symbols are what you think of as the numbers 0 through 9. We then move on to the number 10, but what that actually means is we have a tens column with a 1 and a ones column with a 0. Ten times One plus One times Zero equals Ten. Then you have the hundreds column, the thousands column, and so on. You can put any of the symbols into those columns and do this math and get the result you expect."
"That's because you all know how Base-10 works, even though you didn't know that's what it was called. Most people simply think of this as normal numbers and standard math. The magic is that math works no matter what form you put the numbers in. There are all sorts of other way to handle numbers other than Base-10. The most basic, although most clunky for large numbers, is simply the Unary Number System, or Base-1. In this form there is only one symbol used and how many times you write that number down next to itself is the number you are representing. Four hash marks means the number four. Ten means ten. And so on. As you can see, writing large numbers gets unruly. Imagine trying to write four thousand in Base-1."
"Today we are not going to cover either of these. Instead we are going to cover the next easiest to grasp. That one is what happens to have been chosen to be used in every computer that exists today. Base-2, or Binary as you most likely know it. It has only two symbols used when working with it, normally written as 1 and 0. In computers, however, these are referred to as On and Off. That's because in the computer world those are the two states that transistors and switches can be in. They are either on or off."
"Just as with Base-10 and other numbers systems of this form, you keep adding columns to increase the size of the numbers you can handle. It's what these columns represent that change. As usual, the first column is the ones column, telling you that if you have an on in that column you add 1 to your number total. The second column is your twos column, adding two to the total if you have an on there. The third column, however, is not the threes column. It's actually the fours column. Then you have the eights column. And so on, with each column actually doubling the one before it."
I was starting to get lost in all this, trying to write down notes as fast as I could, but not really understanding much of it any more. At least until he suddenly stopped talking about the numbers and called on us girls to start helping. I had totally forgotten that was going to be a part of this.
"Why don't we make this easier to understand by bringing the girls up here to help." He waved his hand at the open flood. "Can I have the eight of you line up in a row here, facing the class?"
I apparently wasn't the only one who forgot it was coming and wasn't ready. Several of us sputtered, gasped, and/or dropped something before composing ourselves and walking up in front of the rest of the class. It may sound like eight of us walking up front and lining up would empty out a large chunk of the class, but you'd be surprised how many freshman actually take this math class instead of choosing a field already. But it is mostly guys who take it, so the class was still rather full of all guys, and two naked girls, all staring at the eight of us standing in a line.
"In computer programming each of these single units of information that make up the binary numbers is called a bit." He said, going back to his lesson as we stood there waiting. "These girls are each going to be one bit. Since we have eight of them, we can actually make up a full byte, which is the smallest addressable unit of memory used in computing. That's why all your computers and devices talk about how many megabytes or even gigabytes of memory they have. Those are all large collections of bytes, which are collections of bits, which are simply a form of binary numbering."
"With a single byte, like we have with this line of eight girls here, we can form 256 different numbers, ranging from 0 to 255. That's 256 total numbers using only eight numbers that can only be set to One or Zero. It's a very compact way of handling large numbers easily in a form that computers can understand. But you may wonder how these eight numbers can count that high. That's what these girls are going to help show us. They are going to be our byte of information."
He started to walk over to us and stood behind the first girl in line, placing his hands on her shoulders. "Christine here is going to be our Ones column."
He then stepped behind the second girl and said, "Summer is going to be our Twos column."
He then stepped behind me and I could feel his hands on my shoulders as he spoke. "Lisa is going to be our Fours column."
He then continued down the line and said Veronica was going to be the Eights, Cindy was the Sixteenths, Liz was the Thirty-Seconds, Sally May was the Sixty-fours, and Tawnee, down at the end, was our One-Hundred Twenty-Eights. Each of us was going to be part of the larger Byte, representing one of these number columns.
He rounded the end of the line and grabbed some folded papers from his desk. Walking back down in front of us he dropped one of these tented papers in front of each of us. As he dropped each one in front of us, he repeated the numbers we represented, only in reverse order this time. It took me a moment to realize what he was doing, but he was placing signs in front of each of us so the class could easily remember which numbers we were.
He then turned around and stood in front of us, facing the class again. With his back to us he continues with his explanation. "Now that we have our Byte set up, with each one addressed correctly, it's just a matter of setting then to form each of the numbers. Currently they are all set to off, or Zero, which means they all add up to Zero. This is how you represent the number Zero."
He stepped off to the side and faced us again. "Now I just have to turn some of them on, setting them to One, to change the number. We are going to represent turning them on by having them lifting their dresses or skirts as high as they can and showing us how turned on they are. Then, when I turn them back off again they will lower them back down and stand as they are now."
I couldn't believe what I was hearing. His whole plan for us wearing long skirts had nothing to do with keeping us modest while helping him with his demonstration. I wasn't the only one who was shocked by this. I could hear a number of gasps of surprise around me from the other girls. The only one that didn't seem at least a little troubled was Cindy, who actually smiled and looked a little excited.
Professor Harper clapped his hands together, snapping us all to attention again, and said, "Let's get started. Before getting too difficult I'm just going to show you what counting up looks like. Okay, girls, as I walk behind you and tap your shoulder, lift your dress as high as you can. If it's already up, put it back down instead."
He stepped behind Christine again and tapped her on the shoulder. She fidgeted a little, but soon was grabbing the hem of her dress and pulling it up slowly. When her hands were about to chest-height, she stopped. I couldn't really see what she looked like at this point, but she had to of been showing something, since her dress was only about knee-length.
Professor Harper stepped around to in front of her and said, "No, no, that won't do Christine. Lift as high as you can. It has to really stand out that you are different from the rest. Don't stop until you can't lift any higher."
She whimpered slightly and lifted higher, eventually covering her face with the dress, which must have been some kind of relief since she wouldn't have to see any of the boys looking at her. It was pretty clear from where I stood that she was showing everything below her waist, and most likely much of her belly.
"Much better," Professor Harper said, walking back behind her. "With Christine here turned on we have a One set in our Ones column, which means this is the number One. Thank you Christine, you can put it down now."
She wasted no time at all in dropping the dress back down and being fully covered. But Professor Harper also wasted no time in walking to the second girl, Summer, and tapping her on the shoulder. She was right next to me and I could hear her gulp, but immediately started to lift her light, flowing skirt up. Pretty soon it was completely up as far as it would go, and showing off everything below her waist. I could tell from the side that she had a nice little behind on her and was completely shaved up front, which everyone watching could see too. Unfortunately for her, she couldn't raise her skirt high enough to hide her face, so she had to stand there and watch everyone looking at her.
"Now with Summer here turned on her have a One in our Twos column." Professor Harper said from behind us. "Since she's alone, that means we have created the number two."
"Now if I was to just move on again to the next girl," He said and I gulped, readying myself for my turn being exposed. "I would be skipping the number three and moving straight on to number four. That's now proper counting, so how do we form the number three when using binary?"
A few hands shot up, but most of the class simply sat there staring up at him. Well, most likely staring up at Summer's exposed pussy, but you get the idea. Most of the class didn't know any more than I did how to form the number three in this example.
Professor Harper called on one of the boys with their hands raised and he said, "If you turn number one back on you have one plus two, which equals three."
"That's right." Professor Harper said, tapping Christine back on the shoulder again. She resignedly raised her dress again and hid her face. "With these two turned on now we have both a Ones column and a Twos column turned on, which does indeed add up to three. So you can see how counting in Binary is a bit more tricky than just going up the line."
As he spoke I noticed that his hands moved down to rub both the girls on their equally exposed behinds. I guess that would be allowed since it was exposed skin, but it still surprised me to see it done in the middle of a class demonstration like this.
"Now let's keep going a little longer." He said, tapping them both on their shoulders again and letting them lower their clothes. "Next we have the number four, which is another of our base columns again."
On that he tapped me on the shoulder and waited. Having seen how this was going to work, I was ready and simply pulled my dress up as high as I could reach, which I knew was going to show a lot more than just my privates. Kimmy and I had a lot practice pulling on and off my dresses when we were going through them over the weekend, trying to pick out the perfect one for this class, so I knew that if I pulled this one up to my full arm extension it was going to make my breasts pop into view as well. But that's what he told me to do, so that's what I did. I then felt his warm hand come to rest on my behind and start to squeeze it gently as he spoke.
"As you can see, when we hit one of these standard column numbers, the only bit that has to be turned on is that bit for that number. The rest of them are all still in their off state, while the number we want is turned on. This will happen each time we move up to one of these standard groups. Eight, Sixteen, Thirty-Two, and so on. As long as that's the number we want, that's all we have to turn on."
He then stepped away from me, removing his hand from my behind, but not tapping me on the shoulder again. "It's only when we want one of the numbers between them do we need to turn on more than one. So let's keep going a few more, only a little more quickly."
"Five. Come on, you've seen how Lisa's doing it. So do it right. That's better."
I couldn't see a thing with my dress pulled up like this, but I was pretty sure he just moved down and had Christine pull her dress up again. Most likely making her pull it up even higher and possibly exposing her breasts as well. Now I actually wished I could see what was going on. I always thought Christine's little titties were super cute and I'd love to see them right now.
"Okay, Six." I heard him say and there was some slight shuffling again. I then felt his hand land on my ass again and start to knead. I could only assume he was doing the same thing to Summer next to me too. "Now you can see that we have Two and Four both turned on, which is how we get our six."
"Now let's do Seven." This time I audibly heard Christine groan as I was sure she was being told to lift her dress again before the Professor continued. "One, plus Two, plus Four, equals Seven. That's how this kind of counting goes. Now let's finish up with our next standard column number, Eight."
I felt a tap on my shoulder a moment later and was finally allowed to lower my dress again. I saw that both Christine and Summer were also fully covered again, but Professor Harper had moved on passed me and Veronica was now lifting her dress well over her head to show off her goods.
"So, do you think you get how it works now?" Professor Harper asked the class in general, to a smattering of nods and mumbled approval. "Okay, then. Now I'm going to call on you one by one and test your ability to prove it. Who's going to be first?"
A few of the students put their hands up, including Laura, all wanting to be the first one called on. On that he finally tapped Veronica on the shoulder again and let her put her dress back down, as he moved out from behind us to choose one of them to answer.
"Kenny," Professor Harper said, looking down at him with a smile. "You think you understand how this works?"
"Yes, sir." Kenny said, nodding seriously.
"Alright then, let's put that to the test." Professor Harper said, turning back to face us. "I'll set up a number and all you have to do is tell me what number it is."
On that he walked behind us again and started to tap a few of us on our shoulders. Summer, Cindy, Sally, and I all got tapped. We all lifted our skirts and dresses, as instructed, and stood there. The four of us were all on display, and two of us were showing pretty much everything.
There was then a long pause as everyone got a good look at the four of us before Kenny spoke again. "Two, plus four, plus sixteen, plus sixty-four. That's a total of eighty-six."
"Very good." Professor Harper said, walking in front of us again. "Okay, now how about you, Hank."
Professor Harper then walks back behind us and sets up another set of us, leaving some of us exposed and exposing some who were not seen last time. This continued for a few more times until he felt the class understood well enough how to read the numbers, and giving the class more than enough to time look at each and every one of us in the nude. Finally he had us all put our dresses down and be covered at the same time.
"Okay," Professor Harper said, once again addressing the class from in front of us. "You've all shown that you can read the numbers, but we need to test that you truly understand them. Who thinks they can show me they understand?"
Several hands went up and the professor scanned the class before saying, "Okay, Peter, let's see if you can do this. I'll give you a number and you walk up there and make it."
Peter nodded and stepped up next to the professor. "Okay, how do I do this?"
"Easy, I give you a number and you go turn on the right switches to make that number." Professor Harper said, waving Peter back towards us. "Let's start with an easy one. Twenty-five."
"Okay," Peter said and walked up to us. I could see him counting in his head as he walked up the line in front of us. It was funny the way his lips twitched as he counted. He finally stopped in front of Liz and then stepped backwards to stand in front of Cindy. He pointed at her and she simply stared at him.
"Turn on." He said to her, but simply glanced over at the professor.
He gave her a simple shrug, leaving it up to her. She looked back at Peter and said, "It doesn't work that way. That's not how you turn me on."
The class sniggered and Peter blushed.
"Just lift your skirt." He said, trying to compose himself.
"Just like that?" She said with a smirk. "No dinner or anything first? What do you think you are, an Inspector?"
Again the class broke out in laughter and Peter blushed more deeply.
"Professor." Peter said, looking over at him. "She's not cooperating. How can I show you the number if she doesn't do what I say?"
"Didn't see how I did it?" Professor Harper said in a calm voice. "I thought you were paying attention."
Peter flushed again and I saw his shoulders sag as he remembered what the professor did to make it work. "I have to tap them on the shoulders from behind?"
"Either that or you have to do it manually."
The class laughed again and Peter quickly walked behind us. He tapped Cindy on the shoulder and she lifted her skirt. He then tapped Veronica and Christine, who both raised their dresses. Finished, he walked back around and stood next to the professor.
"Good job Peter. You can now take your seat." Professor Harper turned to face the rest of the class. "Okay, everyone line up. You need to all take a turn to show me you can form binary numbers too."
The whole class did as they were told, including the two naked girls and were sent up one at a time with a number they had to form. In addition to making sure the right dresses were up, they had to lower the ones that were left up from the previous number that didn't belong in the new number. Most everyone seemed to get it and answered right, but occasionally the professor had to step in and show them their errors.
When Laura got to the front of the line and took her turn the professor stopped her before she returned to her seat. "Laura, why don't you switch with one of the girls so they can also each get a turn. Take Christine's place and dress and let her have a turn."
"Can't she just put on another dress for this?" Christine said, not wanting to give up hers.
"Hers was confiscated and there are no others here to use." The professor said, "Yours will be returned to you after you've taken your turn as guesser and become a switch again."
She looked annoyed, but slipped off her dress and handed it to Laura, who quickly put it on and seemed relieved to be covered again. Of course Christine was much taller than Laura so the dress came down rather far on her. And when she was made to lift it up—being turned on as a switch—she couldn't actually hold it up by the hem high enough to show her breasts, which seemed to annoy the professor.
After Christine was allowed to take her turn the professor instantly had her retake her dress and place in line, leaving Laura naked again.
"Now, Laura," Said Professor Harper, "Take Summer's skirt and place, so she can take a turn guessing."
Summer didn't argue and simply dropped her skirt to the floor, leaving it where she was standing as she stepped out of it. She then started to pull off her shirt, but the professor put his hand on her arm to stop her, before she could hand it over. "She won't need the shirt to act as a switch." He said, "You can keep that."
Summer smiled and pulled her shirt back on, only having had her lovely breasts exposed briefly.
Laura stepped into the skirt and pulled it up into place, covering her pussy once more. She was then made to turn on during the next test, causing her to lift the skirt. This had the odd effect of exposing her pussy again, but allowing her to cover her breasts, although not her face. Somehow this seemed to strike her as worse than simply being naked, making her blush.
Before summer was allowed to come up and take her turn, Penelope hit the front of the line and took hers. Afterwards the professor made her also swap places with me, so I could take my turn. I had to give up my dress, but I've exposed myself to the class so much by this point that I didn't really care. Since I was part of the example, I was supposed to cut into the line to take my turn sooner, but I was more interested in watching from the audience a little before getting take a turn, so I chose a spot a little ways back.
Seeing it happen from this perspective gave me a new appreciation of just how much we have all been showing while this game was going on. When someone was turned on they really didn't hide anything, especially if they were wearing a short dress. Before I made it up to take my turn I got to watch Summer take her turn and Laura move down to swap with Veronica, putting on her dress.
"Okay Lisa," Professor Harper said as I made it to the front of the line. "Now it's your turn. Your number is one-hundred forty-six."
I quickly did the calculations and figured out who I needed to expose to get the answer but thought I would play with it a little first. I started to point to some of the girls and said, "Okay, you, you and you lift up your skirts."
None of them did, as expected, and the professor said, "You know that's not how this works, Lisa. You have to go up there and turn them on directly."
"I can do that." I said with a smile, and started to walk up to them. But instead of slipping in behind the line and tapping them on the shoulders, I walked directly up to Summer and wrapped my arms around her shoulders, pulling her head towards me and kissing her right on the lips. She seemed surprised at first, but was soon returning the kiss in full. I slipped my hands down her sides and worked them up under her shirt to grope and caress her lovely breasts, flicking the nipples with my fingers.
Slowly I pulled away from her and whispered, "So, are you turned on now?"
Summer licked her lips and slowly nodded, still staring right at me.
"Then you know what to do."
She looked confused for a moment, but then a small smile crossed her lips as it dawned on her. She reached down and slowly started to lift her skirt, showing off her lovely little shaved pussy. I nodded to her, smiling, and then moved down the line.
I next moved in and started to kiss Cindy, who wrapped one leg around me and pulled our bodies close together as we kissed. She was instantly into it, since I was pretty sure she was expecting it after watching me with Summer. My hands were around her sides and back, sliding up and down her warm flesh and causing her shirt to ride up. As soon as her nice little breasts popped out of it I stopped kissing her and slide down to lick and nibble on them. She felt good.
As soon as I pulled away she reached down and pulled up her skirt, not even waiting for me to say anything. I simply smiled at her and licked my own lips as I looked at her sweet little pussy, with the thin stripe of dark hairs above it. I was tempted to drop down and enjoy it a moment, but I still had one more switch I had to turn on.
I finally moved down to the end of the line and approached Tawnee, who smiled at me and seemed to wiggle in anticipation. I wasted no time and moved in to kiss her deeply, while reaching around to squeeze her amazing bubble butt. As I rubbed and squeezed her wonderful ass I slowly slid up her skirt so I could feel her warm flesh on my hands instead of the soft fabric of her covering. Trust me when I say her behind is amazing.
When I finally pulled away I slid my hands off her ass and around her hips, pulling her skirt up more with them. I then handed the edges of her skirt to her, letting her have it and lift it up the rest of the way as I stepped back to look at her cute little bald pussy.
I then walked back over to the professor and said, "I think I turned on the right ones. How did I do?"
He smiled down at me and said, "You did perfect Lisa. You can now go back up and retake your spot in line."
By the time I was back in my dress and ready to perform again it was the next person's turn to go. It seemed that my actions made the remaining students realize that they had more than one way to get us to lift our skirts and dresses, and the rest of the class was a lot more fun for all of us. Nobody was simply tapping us on the shoulder any more.
Some of them were just being more hands on and lifting our skirts or dresses up for us and then telling us to hold it there, but most were getting a lot more handsy, groping us as they made us lift and hold our skirts or dresses up. And some of them even tried to kiss us, the same way I did, wanting to take full advantage of the situation. I had no problem with that and let them, but some of the girls still seemed a little uncomfortable with it. It was amusing to see which girls were more bothered by guys trying to kiss them and which had problems with the girls. Personally, I enjoyed both of them.
I definitely had a lot more hands rubbing and groping my ass and a few guys leaning down to lick my exposed tits once my dress was lifted. The professor didn't seem to try and stop any of them, just standing there and enjoying the show, even ending with the final student being told to form the number two-hundred fifty-five, which required them to turn on all the switches and making all of us expose ourselves at once.
All in all it was a lot of fun, but I was pretty much in a fog for the last half of the class as the teasing was never quite enough to finish me off. When the class finally ended and we were allowed to stop being the example, I rushed back to my dorm and just hoped Kimmy was home. I needed to finish and nobody here knows how to do that for me as well as she does.I was in luck and she was amazing.
Last modified on 2017/4/23 by TruthGirl