Let F : $\{0,1\}$

$->\{0,1\}$

$$ denote the Fibonacci function, specifically, F$($x$)$ is the binary representation

of the n$$th Fibonacci number, where n is the number whose binary representation is x$.$ Prove that F

is a computable function. Note that it is sufficient to specify a multi$-$tape decider that, when started

with x on its first tape and other tapes blank, eventually halts with F$($x$)$ on its first tape. Stick to

implementation description $.$