关于变量公式在循环体外的错误

import java.util.Scanner;
public class TestArray {

    public static void main(String[] args){
        int [] array = new int[]{13,24,35,56,77,89,90};
        Scanner input = new Scanner(System.in);
        int i = input.nextInt();
        int start = 0;
        int end = array.length-1;
        int middle ;//此处middle，只申明变量，不赋值
        int index = -1;
        while(start<end){
            middle= (start+end)/2;//暂不清楚为什么只能在循环体内写入此公式，而不能在循环体外。
            if(i==array[middle]){
                index = middle+1;
                break;
            }
            if(i > array[middle]){
                start = middle+1;
            }
            if(i < array[middle]){
                end = middle-1;
            }
        }

        if(index == -1){
            System.out.println("没找到");
        }else{
            System.out.println("在第"+index+"位");
        }
    }
}