Question 8 ( Conversion from base 5 system into decimal system)
Question 8: Convert \( (413242)_5 \) into equivalent decimal system.
a) 13572 b) 13762 c)13751 d) 13753
percent into a decimal ?
Solution:
Here the number of digits in the given term is 6 – so base 5 will have powers of 5,4,3,2,1 and 0.
To convert given term into a decimal system we multiply first digit i-e 4 with highest power of base 5 i-e with \( 5^5 \) and plus it with second digit i-e 1 multiplied by second highest power 4 of base 5 i-e with \( 5^4 \) – plus it with third digit i-e 3 multiplied with third highest power of base 5 i-e with \( 5^3 \) ………… and so on till – plus the last digit i-e 2 multiplied with last and the least power of base 5 i-e with \( 5^0 \).
Mathematically,
\[ (413242)_5=4\times 5^5+ 1\times 5^4+ 3 \times 5^3+ 2\times 5^2+ 4 \times 5^1 + 2\times 5^0 \]
(Note if any term has power 0 then it is equal to 1, so the last term will be 2 x 1)
Simplifying,
\[ (413242)_5= 4\times 3125+ 1\times 625+ 3\times 125+ 2 \times 25+ 4 \times 5+ 2\times 1 \]
This gives,
\[ (413245)5= 12500+625+375+50+20+20+2 = 13572 \]
So the given number is equivalent to 13572 in decimal system
percent into a decimal ?
Copyright secured by Digiprove © 2020