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

#1**+2 **

*"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_{8 }- 7777_{8.}

The range represented into base 2 is 1000000000_{2} - 111111111111_{2}.

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

I hope this helped,

gavin.

GYanggg
Aug 16, 2018

#1**+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_{8 }- 7777_{8.}

The range represented into base 2 is 1000000000_{2} - 111111111111_{2}.

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

I hope this helped,

gavin.

GYanggg
Aug 16, 2018