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Question 9 (Conversion from octal system to decimal system)

Question 9: Write ​\( (424002)_8 \)​ from octal system to decimal system.

a)141315                b) 141313                c) 141324             d) 141314

Solution:

To write ​\( (424002)_8 \)​ into decimal system we see that there are 6 digits in the number. So it means base 8 will have 6 poweres i-e 5,4,3,2,1 and 0.

We multiply first digit i-e 4 with highest power of base 8 – i-e with ​\( 8^5 \)​plus the second digit i-e 2 multiplied by second highest power of base 8 i-e ​\( 8^4 \)​ plus …………….so on till plus last digit i-e 2 multiplied by last and the least power of the base i-e 8^0.

Mathematically,

\( (424002)_8= 4\times 8^5+2\times 8^4+4\times 8^3+ 0\times 8^2+0 \times 8^1+ 2\times 8^0 \)

\[ (424002)_8= 4\times 32768+2\times4096+4\times 512+0+0+2\times 1 \]

\[ (424002)_8= 131072+8192+2048+0+0+2=141314 \]

 

So, ​\( (424002)_8 \)​ is equal to 141314 in decimal or ordinary number system.

 

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