<p>How would I implement a binary search using just an array? </p>

Ensure that your array is sorted since this is the crux of a binary search.
Any indexed/random-access data structure can be binary searched.  So when you say using "just an array", I would say arrays are the most basic/common data structure that a binary search is employed on.
You can do it recursively (easiest) or iteratively.  Time complexity of a binary search is O(log N) which is considerably faster than a linear search of checking each element at O(N). Here are some examples from
Wikipedia: Binary Search Algorithm
:
Recursive:
```
```
BinarySearch(A[0..N-1], value, low, high) {  
    if (high < low)  
        return -1 // not found  
    mid = low + ((high - low) / 2) 
    if (A[mid] > value)  
        return BinarySearch(A, value, low, mid-1)  
    else if (A[mid] < value)  
        return BinarySearch(A, value, mid+1, high)  
    else
       return mid // found
    }
```
```
Iterative:
```
```
BinarySearch(A[0..N-1], value) {
   low = 0
   high = N - 1
   while (low <= high) {
       mid = low + ((high - low) / 2)
       if (A[mid] > value)
           high = mid - 1
       else if (A[mid] < value)
           low = mid + 1
       else
           return mid // found
   }
   return -1 // not found
}
```
```