Each of the sides of a square S_{1} with area 16 is bisected, and a smaller square S_{2} is constructed using the bisection points as vertices. The same process is carried out on S_{2} to construct an even smaller square S_{3}. What is the area of S_{3} ?
Answer Choices
A. \dfrac{1}{2}
B. 1
C. 2
D. 3
E. 4