You aren't explicitly returning anything from binary_search(), so the return is the value of the last expression executed, which happens to be false. So your $index is always numerically 0, and the word is printed unless it was the first word in the array. Having a binary search return the last index examined can make sense when you may want to insert a new element if it wasn't found, but if you just want to know whether the target was found or not, a boolean return would make more sense.
Your binary_search has a few problems. You need to do the int() after dividing by 2, or your limits will be non-integers and you'll see odd errors. You have an if/else in your while loop, but there are three possible cases (eq, lt, gt) you need to take into consideration. You need to set $high to $cur + 1 - 1, not $cur, or you may have an endless loop.
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