A Written Testimony (Number Systems)

November 22 – 27, 2013

The human civilization have used a lot of different number systems through time. We have tackled some of the common number systems. This includes binary, octal, hexadecimal and of course the number system we now use, decimal number system.

The binary system is based 2. It is only consist of two digits, 0 and 1. This number system needs the least effort in memorizing the symbols since it involves only two digits, but, it also involves the largest string.

Another number system is the octal system. Octa means eight and it is in base 8. It comprises 8 digits, 0, 1, 2, 3, 4, 5, 6, and 7.

Hexadecimal on the other hand is in base 16. Hex means six while deci means ten, thus all in all, it involves 16 digits, namely; 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15. But, unlike the other number systems, this number system also include letters A, B, C, D, E, and F. 10 is represented by A, 11 by B, 12 by C, 13 by D, 14 by E and 15 by F. This number system makes the least string but needs more attention in memorization since it involves sixteen symbols.

Lastly, the most common and widely used number system, the decimal number system. Decima means tenth part, this means it is in base 10. It also involve 10 digits, from 0 to 9. It is the number system that is used nowadays that help us write numbers, solve problems and most of all govern the principal aspect that we use in our daily lives.

Different number systems means different bases, thus, a process of converting one number system to another number system should be learned. This technique is called Base Conversion. It is the process of converting from one base to any other bases.

There also have been several numeration systems of different civilizations. The first one that was tackled was the Egyptian numerals. The same as the decimal system, this numeration system is also base 10. Egyptian number system is hieroglyphic, meaning, it is composed of pictures that represent different values. Staff symbolizes 1, horse shoe for 10, scroll for 100, a lotus flower for 1,000, pointing finger for 10,000, a polliwog for 100,000 and an astonished man for 1,000,000. They just don’t have a symbol for zero.

Babylonian number system on the other hand is in base 60. It is said that they used 60 as base because of its divisibility. One important property that Babylonian number system possess is the presence of unit fractions. The greatest disadvantage of this numeration system is the absence of zero which might make 60 equal to 1 and so on.

One of the most complicated numeration system I encountered is the Chinese number system because of the very-hard-to-memorize symbols. They also have the concept of place value same as the decimal number system.

Mayan numeration system have the concept of zero. It is base 20 and involves very few symbols making them easy to memorize. The unique fact about this numeration system and what makes it challenging is the way it is written. Instead of the left-to-right pattern of writing we are used to, this numeration system is written from top to bottom.

We, Group No. 1 (Number Systems) were assigned to do our presentation for two meetings. This presentation includes (1) a debate about a particular issue under the topic assigned, (2) an audio-visual presentation that will show something about the topic and (3) games that involves number systems. We were given the privilege to manage the time we have and schedule the activities we have to present in class. Then, we came to agree with this schedule:

Day	Time	Activities
January 15, 2014 (Wednesday)	8:45AM – 9:15AM	Debate (Binary System vs Decimal System)
	9:15AM – 9:50AM	Games (Number System Says)
January 17, 2014 (Friday)	8:45AM – 9:15AM	Presentation (Mini movie)
	9:15AM – 9:45AM	Games (Binary Pattern)

January 15, 2014 (Wednesday)

The notion of the debate we had was “What is more useful today and will remain useful for the future generation, Binary or Decimal number system?” The group was split into two parties, one defending the decimal number system, and the other defending the binary number system. Of course, one of us served as the debate facilitator. The debate was supposed to be scripted but since we were given a very limited time, we were not able to rehearse. So, I was very pleased because even if it was spontaneous, it turned out to be okay.

It was said that decimal number system is the universally used number system nowadays thus, making it more preferable to use. This number system is also the most convenient one if we are to apply complex mathematics. The point is, mathematics is a language, and language do not change abruptly, it is gradual. And when you have to change a language, there is one important factor involved that is the hardest part to manage, the community. It means that when changing a language, so as the community.  Well for me it is the hardest part because you can’t easily teach an entire community a whole new language.

Binary system on the other hand pushed the fact that human beings are entering the digital world, world of computers. Computer uses binary digits as their internal codes, and basically, if we are to go deeper into the computer world, we should learn how to use binary number systems. Their party mentioned that it is always good to change, we just need to learn how to.

But, let’s just be realistic and know that change is always for the better, but it’s not that easy to change, cause if it is, the world should have been much better than it is now.

The debate took more or less 30 minutes, thus, to consume the remaining time, we facilitated a game entitled “number system says”. It is a base conversion game, but to imply a little bit of challenge and to make it fun, we decided to have it outdoor. We gave phrases as clues that will lead the groups to where we hid the problems they need to solve. Thus, in order for them to solve the problems, they must first unearth the hidden message. I was very much aware that handling this kind of activity is hard because once they’re sent to the field, you cannot control them anymore, so we came up with a rule that states that no talking is allowed. It even improved their team work and listening skills because in order for them to communicate as a group, they should really pay attention since only hand and body gestures are allowed. It came out to be effective because the groups were noiseless until the end of the game. Each problem is worth five points, two points for uncovering the clue and three points for solving the problem. It was all in all fun. This happen to be the scores of each group:

Algebra           - 12 pts

Computers       - 18 pts

Geometry        - 17 pts

Statistics          - 6 pts

January 17, 2014 (Friday)

Today, we had the mini movie that we were able to come up with from a week of preparation. It was about a student which happen to be very smart in Mathematics. One day, he received a phone call, telling him that the entire school is planted with bombs and the only thing he can do to stop the bombs from exploding is to play the bombers game. He decided not to tell anybody except his best friend whom he trusted with all his life. The bomber prepared problems for the student to solve, all of which involved number systems. Since he was that smart, he was able to solve the problems, win the game, and stop the bomb form exploding but he was still unable to discover who the crazy bomber was, until... That was the mystery that was he was not able to solve using Mathematics. This group presentation required a lot of time. We’ve been shooting for the mini movie for more than a week and it was really hard to maintain the continuity of the film. The movie was also informational because we inserted clips about the history and some information about topic assigned to us. It turned out to be good according to my classmates and I’m very glad about it.

The mini movie consumed 25 minutes and again, to maximize the time we have, we facilitated another game. It was a memorization game that still involves number systems. The game was composed of two rounds. The first round was easy because it involved binary numbers, thus only two digits are included. The players just need to supply an additional binary digit to the given binary digits, and memorize them all until someone get them wrong. The second round was the same with the first round except that instead of binary numbers, decimal numbers are involved, and not just that, decimal number plus one word. The fun thing about this game is when somebody got it wrong, he/she should sing a song with a number in it. This was really challenging and my classmates did have fun. Each people that will remain in the game will earn their group 1 point. These are the scores of the groups:

Algebra           - 2 pts

Computers       - 3 pts

Geometry        - 0 pts

Statistics          - 1 pts

 “Number systems” is a very interesting topic. It mainly became the backbone or the representation of Mathematics for a very long time. Number systems have watched the human civilization grow to what state we are now. There have been different number systems, and all of them gave way and opportunities for us to improve, discover and learn more. It helped us unravel the wonders of Mathematics.