67. Add Binary

class Solution {
    public String addBinary(String a, String b) {
      StringBuilder sb = new StringBuilder();
      
      int i = a.length() -1;
      int j = b.length() -1;
      int carry = 0;
      
      while( i >= 0 || j >= 0){
        int sum = 0;
        sum += carry;
        if( i >= 0){
          sum += a.charAt(i) - '0';
          i--;
        }
        if( j >= 0){
          sum += b.charAt(j) - '0';
          j--;
        }
        
        sb.append(sum % 2);
        carry = sum / 2;
      }
      
      if( carry == 1){
        sb.append(carry);
      }
      
      return sb.reverse().toString();
        
    }
}



////  a.charAt(i) - '0'
///// sb.append()
////// sb.reverse().toString();

this one is two strings added together. Still need to add the 

Two element from two string from the last digit 

 

Use a string builder to add backwards, by that, I mean, 

Use append to append the new element, so its reverse order 

 

Use while outside when the two numbers are not exhausted 

 

And use two ifs to check if number a and number b 

Are not exhausted, and add the current digit if valid 

 

Append the sum % 2

And carry = sum / 2 

An carray is added to the next level sum 

 

 

 

11 + 1 = 100 

When the 11 and 1 length are all exhausted, we check if the carry is 1 , carry can only be 1 or 0, if carry is 1, then we know we need to append 1 , if its 0, we don’t need to do anything 

 This is similar to plus one that problem,

 

At the end, we need to reverse the string , since we append the sum at the tail 

 

 

 

 

 

Given two binary strings, return their sum (also a binary string).

The input strings are both non-empty and contains only characters 1 or 0.

Example 1:

Input: a = "11", b = "1"
Output: "100"

Example 2:

Input: a = "1010", b = "1011"
Output: "10101"

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