Base Conversions - An Introduction

Base Conversions - A topic that students (especially, those doing IT) are bound to encounter during their course of study. It might be a real headache for some students to master these conversion techniques, that is, the steps involved in converting a number from one base to another, etc.. (believe me, i've been there :] ). 

However, once you get into it, you start to realize that its not so bad after all. This blog is aimed at helping students gain a better understanding of this topic and answer any questions regarding it. Along the way, you will find easy to follow steps (for converting between different bases), example workings and many exercises (to test your understanding). 

By the time you are finished with the guides featured here, you will be somewhat of an expert on this topic. All that you need to do is be patient and practice a lot (easier said than done, I know). And who knows? You might even enjoy doing these calculations (too optimistic eh? Well, you never know... miracles do happen!). Let's get started.     

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There are many number systems used nowadays. The most commonly used numbering systems are listed below.

 

• Decimal -- The most widely used numbering system. It uses 10 distinct symbols (0,1,2,3,4,5,6,7,8,9) to represent any value, big or small. Thus, it is also known as the base-10 numeral system. That is, any decimal value has '10' as its base. 
  eg; 128₁₀
  
  
• Binary -- The numeral system used and understood by computers. It uses only 2 distinct symbols (0,1) to represent any value. Thus, it is known as the base-2 numeral system. That is, any binary value has '2' as its base.
  eg; 101011₂
  
  
• Octal -- This is the base-8 numeral system. It uses 8 distinct symbols (0,1,2,3,4,5,6,7) to represent any value. An octal value has '8' as its base.
  eg; 24₈ 
  
  
• Hexadecimal -- This is the base-16 number system. It uses 16 distinct symbols (0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F) to represent any value. A hexadecimal value has '16' as its base.
  eg; 7A7₁₆ 
  

The following table lists the first sixteen decimal integers (0 - 15) and their equivalent binary, octal & hexadecimal values.