Update Add Binary

Add Binary

@@ -6,33 +6,29 @@ class Solution {
 public:
     string addBinary(string a, string b) {
         // Make both strings of equal length by prepending zeros
-        if(a.size() > b.size())
+        if (a.size() > b.size()) {
             b = string(a.size() - b.size(), '0') + b;
-        else if(a.size() != b.size())
+        } else if (a.size() < b.size()) {
             a = string(b.size() - a.size(), '0') + a;
+        }
 
         string result(a.size(), '0'); // Initialize result string with zeros
         bool carry = false; // Initialize carry to false
 
-        for(int i = a.size() - 1; i >= 0; --i)
-        {
-            if((a[i] == '1' && b[i] == '0') || (a[i] == '0' && b[i] == '1'))
-            {
-                result[i] = carry ? '0' : '1';
-            }
-            else if(a[i] == '0' && b[i] == '0')
-            {
-                result[i] = carry ? '1' : '0';
-                carry = false;
-            }
-            else if(a[i] == '1' && b[i] == '1')
-            {
-                result[i] = carry ? '1' : '0';
-                carry = true;
-            }
+        // Iterate from the last character to the first
+        for (int i = a.size() - 1; i >= 0; --i) {
+            int sum = carry; // Start with the carry
+            sum += (a[i] - '0') + (b[i] - '0'); // Convert char to int and add
+
+            // Determine the resulting bit and the new carry
+            result[i] = (sum % 2) + '0'; // Current bit
+            carry = sum / 2; // Update carry
         }
-        if(carry)
+
+        // If there's a carry left, prepend it to the result
+        if (carry) {
             result = '1' + result;
+        }
 
         return result;
     }