[001] - Number Systems
In our everyday lives, we use Decimal Numbers whenever we deal with them. That is, we use a number system in which the digits range from 0 to 9 – a total of ten digits (hence the name, decimal). However, there are many number systems that are in existence, and before we define them, let us take a look at the features that define a Number System.
Each Number System has a base, which is determined by the number of digits that make up that system. For example, the decimal number system consists of ten digits; hence, its base is ten. Base is also known as the radix, and is denoted by the letter r.
The value of a number in a number system is interpreted as the sum of the face values of various digits multiplied by the radix raised to the power of the index of the digit, starting from right. For example, to interpret the value of the decimal number 465, we may write:
In order to distinguish between various number systems, the digits of the number are enclosed in parenthesis, and its radix is inserted as the subscript. For example, we may write 
to denote the decimal number 465.
Various Number Systems
As stated before, there are a variety of Number Systems, decimal being one of them. Let us learn about all of them.
Binary Number System
As the title suggests, the Binary system consists of only two digits, 0 and 1. Its radix, therefore, is two. This number system is used in all kinds of electronic devices to perform various computations. To interpret its value, we will write:
Octal Number System
This system has a radix of 8, so the digits range from 0 to 7. Its value is interpreted in pretty same way as the other systems. For example:
Hexadecimal Number System
The hexadecimal number system has a radix of 16, and the digits now range from 0 to 9, and afterwards from A to F. Here, A to F represent the decimal 11 to 15. The value of a hexadecimal number will be interpreted like this:
These are the number systems that exist. My next post in this series will deal with converting numbers from one number system to another.
[...] are represented using a variety of number systems, including Binary, Octal, Decimal, and Hexadecimal. However, they can be easily converted from one [...]
[002] - Number Conversions across various Number Systems (Part 1) at APS 2.0
10 Aug 08 at 7:21 pm
I landed here from Freya’s blog..
APS2.0? may be a year or six months or less after, you would enter into 3rd yr of applied physics..will the title change or a new series would begin?
Now the real part, this blog is appreciative and rare to find bloggers interests on technos.. whole world is all numbers numbers and number system. Take a plant, the arrangement of leaves or flowers is factorial, fibonacci or more..
Nice blog..neatly written and understandable..
Happy blogging
Prema
Prema
22 Sep 08 at 4:13 pm