By the end of this unit, you should be able to

BASES AND NUMBER REPRESENTATION

UNIT 2: BASES AND NUMBER REPRESENTATION

By the end of this unit, you should be able to:

• 
  understand the different number systems that exist.
  
• 
  perform conversions from one number system to another.
  
• 
  perform operations like addition and subtraction in different number systems.
  

1.1 Number Systems

There are two classes of number systems:

1. 
   Roman number system is position independent.
   
2. 
   Modern number systems are based on positional notation (place value)
   
   • 
     Decimal system: system of positional notation based on powers of 10.
     
   • 
     Binary system: system of positional notation based powers of 2
     
   • 
     Octal system: system of positional notation based on powers of 8
     
   • 
     Hexadecimal system: system of positional notation based powers of 16
     

1. 
   Decimal Number System
   

The origin of decimal or base 10 number system comes from counting on the fingers.

• 
  “Digit” from the Latin word digitus means “finger”
  

Positional Notation: Base 10



1.1.2 Why Binary?



Early computer design was decimal

• 
  Mark I and ENIAC
  

John von Neumann proposed binary data processing (1945)

• 
  Simplified computer design
  
• 
  Used for both instructions and data
  

Natural relationship between on/off switches and calculation using Boolean logic