Here in the United States we use a base10 system for many things… certainly we count using a base10 numbering system. Our currency is base10. I can remember the big push in the late ‘70s to move to the metric system, which by the way is a base10 system. Yet we may not realize that there are many different numbering systems ingrained in our society. We use an English system to express units of measure (length). Which in many ways is based on a Roman system of measurement! An example being the mile… Originally based on the Roman mile (5000 feet), in 1592 it was extended to 5280 feet to make it an even number (8) of furlongs (wikipedia.org, 2010). By the way… The distance between the rails on a high-speed train line is 143.5 centimeters. Why? Because that was the distance betweens the wheels of Roman chariot. That was the distance needed to fit two horses side by side in front of the chariot.
In IT, we are familiar seeing different numbering systems. We see both Base2 (binary) and Base16 (Hexadecimal) numbering system quite a lot.
The binary number system contained just two values, 1 and 0. George Boole is considered by many as the father of modern day computing. It was his work with logic that ultimately boils down logic and the math behind it to simple yes or no (1 or 0). This can make computing numbers extremely fast. If one thinks in terms of electricity switches you either have an on or an off position. Computer microchips are designed in such a fashion that depending of the state of the signal (1 or 0) a logic pattern can be computed and the software then executed. We in IT often find behind this logic. It is so ingrained in our beings that it is often hard for us to factor in the randomness that plays such a large part in life. Why? Because we are surrounded by 1’s and 0’s. Yes we all know that computers use on and off as a basic premise of computer code… But did you know that CD/DVD/BluRay Discs are perfect illustrations of the use of the binary system. They are encoded by a laser punching holes in the foil membrane embedded within the protective plastic casing. These holes (or pits) represent a 0 (or no signal) and the untouched foil (or non-pit areas) represents a 1. When played back the software converts this binary stream into the music or movies that we’ve come to enjoy!
We also come across hex numbers quite often as well! The hexadecimal number system complements the binary system. Each hexadecimal digit represents four binary digits (bits) (also called a “nibble”), and the primary use of hexadecimal notation is as a human-friendly representation of binary coded values in computing and digital electronics (wicketkeeper, 2010) We see hex used when looking at MAC addresses. We use hexadecimal representation for RGB colors in Photoshop, HTML or CSS documents. We will be using hexadecimal numbers when writing out Ipv6 addresses! If you’ve ever used a packet capture tool such as Wireshark. Network packets as written in hexadecimal as well. 192.168.1.1 can be represented as c0 a8 01 01. A lot less characters that need to be put out onto the wire.
Different number systems are be fundamentally thought of as ways to keep track of information in the most efficient way that the numbers can be grouped together.
Resources:
Various, (2010, April, 10) English Units, Retrieved on April 28th, 2010 from http://en.wikipedia.org/wiki/English_units
Various, (2010, April 28th), Hexadecimal, Retrieved on April 28th, 2010 from http://en.wikipedia.org/wiki/Hexadecimal
