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
solve math problems
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.
solve math problems!
Copyright secured by Digiprove © 2020