Brief Introduction on Number Systems

In the Arabic number system, we have ten digits (from 0-9) and we can make as big a number as we want with these. We use all ten digits to count to nine, then we combine them to make bigger numbers. So we never run out of numbers, as long as there is room to write them down.

The ancient Egyptians didn't think this. They had a simple line to mean one, like us, but instead of a new symbol for two, they used two lines. There were three lines for three, four lines for four, and so on, up to nine lines for nine. By now, there were rather a lot of lines! So they introduced a new symbol for ten. Then they carried on adding lines for units and ten symbols for ten, until they got to a hundred, which needed a new symbol. This sort of system is called unary. It is common among ancient civilizations. One advantage of unary systems is that it doesn't matter what order you write the number. You can jumble them up and you can still work out what they mean. But in our system, 123 mean something different to 321. The Egyptians used ten as a base for their number systems, just like us. We have ten fingers on our hands, so base 10 is common.

http://gwydir.demon.co.uk/jo/numbers/egypt/intro.htm
Let’s see another number system, Babylonian numerals.
The Babylonian civilization in Mesopotamia replaced the Sumerian civilization and the Akkadian civilization. We give a little historical background to these events in our article Babylonian mathematics. Certainly in terms of their number system the Babylonians inherited ideas from the Sumerians and from the Akkadians. From the number systems of these earlier peoples came the base of 60, that is the sexagesimal system. Yet neither the Sumerian nor the Akkadian system was a positional system and this advance by the Babylonians was undoubtedly their greatest achievement in terms of developing the number system. Some would argue that it was their biggest achievement in mathematics.
Often when told that the Babylonian number system was base 60, people first reaction is: what a lot of special number symbols they must have had to learn. Now of course this comment is based on knowledge of our own decimal system that is a positional system with nine special symbols and a zero symbol to denote an empty place. However, rather than have to learn 10 symbols as we do to use our decimal numbers, the Babylonians only had to learn two symbols to produce their base 60 positional system.
Now although the Babylonian system was a positional base 60 system, it had some vestiges of a base 10 system within it. This is because the 59 numbers, which go into one of the places of the system, were built from a 'unit' symbol and a 'ten' symbol.
Here are the 59 symbols built from these two symbols

http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Babylonian_numerals.html

Any number less than 10 had a wedge that pointed down.

Example:      4     

The number 10 was symbolized by a wedge pointing to the left.

Example:     20     

Numbers less than 60 were made by combining the symbols of 1and 10.

Example:      47     

As with our numbering system, the Babylonian numbering system utilized units, ie tens, hundreds, thousands.

Example:     64     

However, they did not have a symbol for zero, but they did use the idea of zero. When they wanted to express zero, they just left a blank space in the number they were writing.

When they wrote "60", they would put a single wedge mark in the second place of the numeral.

When they wrote "120", they would put two wedge marks in the second place.

Following are some examples of larger numbers.

Example:	79883
	(22*6022)+(11*60)+23

Example:	5220062
	(24*603)  +  (10*602)  +  (1*60)  +  2

http://www.math.wichita.edu/history/topics/num-sys.html#babylonian

Maya numerals are another interesting one that contains a lot of wisdom of ancient Mayans.
Maya numerals are vigesimal (base-twenty) numeral system used by the Pre-Columbian Maya civilization.
The numerals are made up of three symbols; zero (shell shape), one (a dot) and five (a bar). For example, thirteen is written as three dots in a horizontal row above two horizontal lines stacked above each other.

This number written in Arabic would be 1.10.2.14.3 (McLeish, 1991, p. 129).

The Mayan's were also the first to symbolize the concept of nothing (or zero). The most common symbol was that of a shell ( ) but there were several other symbols (e.g. a head). It is interesting to learn that with all of the great mathematicians and scientists that were around in ancient Greece and Rome, it was the Mayan Indians who independently came up with this symbol that usually meant completion as opposed to zero or nothing. Below is a visual of different numbers and how they would have been written:

In the table below are represented some Mayan numbers. The left column gives the decimal equivalent for each position of the Mayan number. Remember the numbers are read from bottom to top. Below each Mayan number is its decimal equivalent.

8,000
400
20
units
	20	40	445	508	953	30,414

It has been suggested that counters may have been used, such as grain or pebbles, to represent the units and a short stick or bean pod to represent the fives. Through this system the bars and dots could be easily added together as opposed to such number systems as the Romans but, unfortunately, nothing of this form of notation has remained except the number system that relates to the Mayan calendar.

For further study: The 360 day calendar also came from the Mayan's who actually used base 18 when dealing with the calendar. Each month contained 20 days with 18 months to a year. This left five days at the end of the year that was a month in itself that was filled with danger and bad luck. In this way, the Mayans had invented the 365-day calendar that revolved around the solar system.

References.

1. McLeish, J. (1991). The story of numbers. New York, NY: Fawcett Columbine.
2. Ortenzi, E. C. (1964). Numbers in ancient times. Portland, ME: J. Weston Walch.
3. Roys, R. L. (1972). The Indian background of colonial Yucatan. Norman, OK: University of Oklahoma Press.
4. Thompson, J. E. S. (1967). The rise and fall of Maya civilization. Norman, OK: University of Oklahoma Press.
5. Trout, L. (1991). The Maya. New York, NY: Chelsea House Publishers.

Then, let’s see Hindu-Arabic numeral system.

The Hindu–Arabic numeral system or Hindu numeral system is a positional decimal numeral system developed between the 1st and 4th centuries by Indian mathematicians. The system was adopted by Persian Muslim mathematician (Al-Khwarizmi's c. 825 book On the Calculation with Hindu Numerals) and Arab mathematicians (Al-Kindi's c. 830 volumes On the Use of the Indian Numerals) by the 9th century. It later spread to the western world by the High Middle Ages.

The system is based upon ten (originally nine) different glyphs. The symbols (glyphs) used to represent the system are in principle independent of the system itself. The glyphs in actual use are descended from Indian Brahmin numerals, and have split into various typographical variants since the Middle Ages.

These symbol sets can be divided into three main families: the Indian numerals used in India, the Eastern Arabic numerals used in Egypt and the Middle East and the West Arabic numerals used in the Maghreb and in Europe.

http://en.wikipedia.org/wiki/Hindu%E2%80%93Arabic_numeral_system

Why would we need to learn number systems? There are a couple of reasons. First, as human being, we use words and letters to speak to one another. In the same way we need to make electronic devices such as computers understand what we say or what we want it to do. So to make computer understand we use number system. We use ordinary language to type on computer but these are translated into computer language i.e. binary language. Second, the significance of being aware of the history development of number system is a great way for students to combine their knowledge and concepts on items, which also could inspire student’s motivation to explore math with fun by themselves.