Number System

Question

What is the minimum number of bits required to represent (516)base 7 in base 4.

Comments

$5$?

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log₄(776)=5

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@Anu it should be $\log _{4}\left ( 5 \times 7^{2}+1 \times 7^{1} +6 \times 7^{0} \right )=\log _{4}(258)=5$

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yes bro its correct soln

Answer 1

(516)₇ = 5 * 7² + 1 * 7¹ + 6 * 7⁰ = 258

We know

4^{0 =}1 ,

4^{1 =}4,

4^{2 =}16 ,

4^{3 =}64 ,

4^{4 =}256 &

Since we have to represent the number 258 in base 4, 5 digits is enough.

PS: Using n digits, I will be able to represent numbers from ( 0 to rⁿ-1 ) . For example Using 4 digits of base 4 , I can represent numbers from 0 to 4⁴ - 1, ( i.e., 0 to 255 ). In our case the number is slightly greater than 255 , so we need one more digit to represent the number, Hence 5 digits

Answer 2

(516) base 7  = (10002) base 4

so according to this answer is 5.

plz, comment if wrong

Comments

correct