Binary 101

Number Theory Level 2

What is ( 10 1 101 ) 2 \left ( 101^{101} \right )_{2} ?

Note: The subscript implies base 2, but your answer should be in decimal.

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The answer is 3125.

Geoff Pilling by Geoff Pilling , 53, USA

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1 solution

Geoff Pilling
Apr 16, 2016

( 101 ) 2 = ( 5 ) 10 ( 101 )_{2} = ( 5 )_{10} . And 5 5 = 3125 5^5 = 3125

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