Let $S$ be the set of all positive integers that have four digits in base $2$. What is the sum of all of the elements in $S$, when expressed in base $2$?
Question:
Let $S$ be the set of all positive integers that have four digits in base $2$. What is the sum of all of the elements in $S$, when expressed in base $2$?
Answer:
Let's think step by step.

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Let $S$ be the set of all positive integers that have four digits in base $2$. What is the sum of all of the elements in $S$, when expressed in base $2$?
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