solve-x-4-2-100100-2-find-x-and-leave-answer-in-base-2-

Question Number 171867 by Mikenice last updated on 21/Jun/22

s o l v e : x_{4}^{2} = 100100_{2}, f i n d x a n d l e a v e a n s w e r i n b a s e 2 .

Answered by floor(10²Eta[1]) last updated on 21/Jun/22

100100_{2} = 2^{5} + 2^{2} = 36

x_{4} = a_{n} 4^{n - 1} + a_{n - 1} 4^{n - 2} + \dots + a_{2} 4 + a_{1}, a_{i} \in {0, 1, 2, 3}

x_{4}^{2} = 36 \Rightarrow {(a_{n} 4^{n - 1} + \dots + a_{1})}^{2} = 36

a_{n} 4^{n - 1} + \dots + a_{1} = 6 = 4^{1} . 1 + 4^{0} . 2

x_{4} = 12_{4}