\[S = \frac {1}{2^1} + \frac {1}{2^2} + \frac {1}{2^3} + \ldots + \frac {1}{2^7}. \]

If \(S = \frac {a}{b}\), where \(a\) and \(b\) are positive, coprime numbers, what is the value of \(a+b\)?

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