Each of the numbers w, x, y, and z is equal to either 0 or 1. What is the value of w + x + y + z ?
(1) \frac{w}{2} + \frac{x}{4} + \frac{y}{8} + \frac{z}{16} = \frac{11}{16}
(2) \frac{w}{3} + \frac{x}{9} + \frac{y}{27} + \frac{z}{81} = \frac{31}{81}
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