Converting Hexadecimal to Octal: A Simple Guide

Ever feel lost trying to change numbers from one form to another? (like me when I first started!) Hexadecimal and octal are two number systems, and understanding how to switch between them can be really helpful. Don't worry, we'll walk through the steps like it's nothing.

What are Hexadecimal and Octal Numbers?

Source: dotnettutorials.net

• Hexadecimal uses 16 digits (0-9 and A-F)
• Octal uses 8 digits (0-7)

(Think of them as different languages for numbers!) Decimal (what we normally use, like 10, 20, 30), is just another way to express amounts. This process is also common for computers, for representing memory address.

Why Convert Between Systems?

Source: w3resource.com

Different contexts demand different formats for the same number. For instance, certain computer languages favor hexadecimal representation for memory addressing, whilst others prefer octal for displaying character sets. Converting these representations can allow data exchange. Understanding conversion lets you "talk" to the computer on their level.

Steps to Convert Hexadecimal to Octal

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This isn't as tricky as you think, just take it one step at a time. Let's do this step by step.

1. Understand the Relation: Hex to Decimal then Decimal to Octal

First, let's turn your hexadecimal number into a familiar decimal number. After converting to a decimal equivalent , convert to octal (base-8). Think of a bridge, hexadecimal to decimal is one side of the bridge and the other side is from decimal to octal.

2. Hexadecimal to Decimal Conversion

• Assign Values: Each hexadecimal digit has a corresponding decimal value. (A = 10, B = 11, C = 12, D = 13, E = 14, F = 15).

• Convert Digits to Decimal Equivalent: Every Hexadecimal place value correspond to decimal equivalents and have to multiply with those values. This is actually like working with money. For instance if we write 7A2 = in hex and want convert to Decimal, then

  1. first find out the decimal values corresponding to each hex character , like A's equivalent = 10

  2. now calculate for each character to multiply each value with place holder( powers of 16):

  Decimal equivalent = (7 × 16²) + (10 × 16¹) + (2 × 16⁰)

  • This part is pretty important. Understand that this gives you the decimal form (as you already understand this.) Try it with an example! Try changing hex (1A) to decimal form!

• Calculate: Simply solve that expression to get the Decimal representation of the Hexadecimal input .

3. Decimal to Octal Conversion

• Dividing by 8: The division by 8 process. It’s basically reverse of your usual process (multiplication). For this purpose remember your octal table of multiplication tables as 2, 4, 6, 8

• Writing down remainders: In order to get an equivalent Octal representation from your converted Decimal value. Take each remainder while dividing by 8.

• Arrange in correct order: Once all remainders is collected in correct manner arrange in right format from top (or from the bottom if working from bottom!) and we are ready! For example, for converting decimal 3200 to Octal:

1. 3200 ÷ 8 = 400 Remainder 0. Write down remainder 0

2. 400 ÷ 8 = 50 Remainder 0. Write down 0

3. 50 ÷ 8 = 6 Remainder 2. Write down 2.

4. 6 ÷ 8 = 0 Remainder 6. Write down 6.

• Write out the Octal: Now that all of your remainders are on paper combine in order to form the answer octal. Which is Octal 6200 in this instance!

4. Example

Source: dotnettutorials.net

Let's say we have the hexadecimal number "1A".

1. Convert 1A to Decimal:

   1A (hex) = (1 × 16¹) + (10 × 16⁰) = 1 × 16 + 10 × 1 = 26 (decimal).

2. Convert 26 (decimal) to Octal:

   1. 26 ÷ 8 = 3 remainder 2
   2. 3 ÷ 8 = 0 remainder 3
   • So the octal equivalent of 26 is 32.

   

   Source: mathmonks.com

Question for Review!

Now that you’ve been exposed to this process. Let me try to stump you (haha!). Can you convert the hex 1F to its octal equivalent! I want to hear your results! Give a shot by doing the process yourselves.

Common Mistakes & Solutions

• Confusion on the Power of Digits: Be extremely careful in applying the correct power to digits during calculation.
• Mismatch in Position Value: Misremember or incorrectly determine values at their places that they occupy.

Key takeaways and Practical Uses:

Remember! Learning how to convert number systems can actually be helpful, when for example, dealing with the computer system!

Conversion table examples (Small):

You have the ability to now convert between number system and are confident, right ?

I sincerely believe, after learning all these processes, this may assist you for everyday tasks like using spreadsheets or any applications that require to operate with hexadecimal values and that way you feel confident!

Let me know if you have more questions; I would be happy to help further. Keep converting those hexadecimal to octal!