Positional Number Systems

Question

The problem is: Convert number 3424 base 5 to base 6 in Positional Number Systems

Can you please describe it step by step

Thank you in Advance!

Answer 1

Hi

The best and easy way is to pass through decimal and readable system, so we convert 3424 base 5 to base 10:

3424₅=(4*(5⁰)+2*(5¹) +4*(5²) +3*(5³))₁₀

=(4+10+4*25+3*125)₁₀

=(4+10+100+375)₁₀

=489₁₀

Then we will transform 489₁₀ from base 10 to base 6, to do so we will make successive euclidean division by 6 as fellow:

step 1: 489//6 give 81 and 3 remainder

step 2: 81//6 give 13 and 3 remainder

step 1: 13//6 give 2 and 1 remainder

so from step 1 489₁₀=3+(81*6) we replace 81 with it's value from step 2

we get: 489₁₀=3+(((13*6)+3)*6) we replace 13 with it's value from step 3

we get 489₁₀=3+((((2*6)+1)*6)+3)*6) the expression now contains only the power of 6 and remainders<=6

so we can develop it to 489₁₀=3*6⁰ + 3*6¹ + 6² + 2*6³

finally 489₁₀=2133₆

I hope that you appreciate Good Luck