icon, 245 bytes

Result [link]

AC

Code [DL]

procedure main()
	ai := read() 
	d := 50
	a :=  reverse(ai[1:d+1])
	b := reverse(ai[d+1:d*2+1])
	s := 0
	
	every i := 1 to d do {
		s *:= 2
		s +:= a % 10
		a /:= 10
	}
	every i := 1 to d do {
		s *:= 2
		s +:= b % 10
		b /:= 10
	}
	write(s)
end

stdin

1000111010010110110001100100110011110101010000101110100011010011100001001001100010011011111011100001

stdout

706066347452196732955498495713

stderr

strace