The Base

Number Theory Level 2

Which of the following options(in base-10) equal to 5 1 2 ? 51_2?

Note: \textbf{Note:} In this question,it is assumed a 2 digit number of the form x y ‾ b \overline{xy}_b is expressed in base b b .

12 11 22 The question is flawed 13

Anandmay Patel by Anandmay Patel , 20, India

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3 solutions

Prince Loomba
Oct 20, 2016

51 in base 2 does not exist. Base 2 numbers are only written with digits 0 and 1.

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Anandmay Patel
Oct 20, 2016

Base-2 numbers can only be written with digits chosen from the set {0,1}.

In general,base-b numbers are expressed by digits from the set {0,1,2,3,4,........,b-2,b-1}

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Navneet Prabhat
Oct 21, 2016

Any of the digits in a number can not be greater than its base.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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