# 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. Copyright secured by Digiprove © 2020
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