Data Representation Using Binary Digits

Decade	1970s	1980s	1990s
2000s
Order of magnitude in Storage capacity	Thousands	Millions	Billions	Trillions
Prefix	Kilo (10^3)	Mega (10^6)	Giga (10^9)	Tera (10^12)
Abbreviation	K	M	G	T

In terms of storage, more is better—which means more information in the form of both data and programs that act on that data can be stored. Corresponding to the growth in storage capacity, memory capacity is also increasing. Moreover, memory technologies are getting smaller, lighter, and faster, for about the same price. You will learn more about storage and memory technologies in the next unit of this course.

1.3.2 Number Systems

• 
  Decimal
  
• 
  Binary
  
• 
  Hexadecimal
  

The world of computing uses several number systems to represent data. While the decimal system, also known as base10, will be familiar to people, as it is the numbering system used in everyday life, binary (base2) and hexadecimal (base16) are common number systems used in computing today.

Decimal

We will start our discussion on number systems by examining the decimal system as an example of a number system. The decimal number system contains ten values- 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each number in the decimal number system can be broken into digits by their "place" in the number. Using the number 43,872 as an example, 2 is in its 0th place, 7 is in its first place, 8 in its second, 3 in its third, and 4 in its fourth. Each place has a value that can be represented either exponentially or by its decimal values. The following table shows the exponential and decimal representation for each place in the number 43,872.

Place	4th	3rd	2nd	1st	0th
Digit	4	3	8	7	2