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A certain integer has 4 digits when written in base 8. The same integer has d digits when written in base 2. What is the sum of all possible values of d?

Guest Aug 16, 2018

Best Answer 

 #1
avatar+964 
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"A certain integer has 4 digits when written in base 8. The same integer has \(d\) digits when written in base 2. What is the sum of all possible values of \(d\)?"

 

Four-digits base 8 numbers range from 1000- 77778.

 

The range represented into base 2 is 10000000002 - 1111111111112.

 

Therefore, the minimum is 10 digits, and the maximum is 12. 

 

I hope this helped,

 

gavin. 

GYanggg  Aug 16, 2018
 #1
avatar+964 
+2
Best Answer

"A certain integer has 4 digits when written in base 8. The same integer has \(d\) digits when written in base 2. What is the sum of all possible values of \(d\)?"

 

Four-digits base 8 numbers range from 1000- 77778.

 

The range represented into base 2 is 10000000002 - 1111111111112.

 

Therefore, the minimum is 10 digits, and the maximum is 12. 

 

I hope this helped,

 

gavin. 

GYanggg  Aug 16, 2018

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