diff --git a/README.md b/README.md
index 6e02f8b..5922e1d 100644
--- a/README.md
+++ b/README.md
@@ -46,8 +46,8 @@ $ pnpm test twoSum.test.ts
 12. [分治 (Divide and Conquer)](./algorithms/12.divide-and-conquer/README.md)
 13. [回溯 (Backtracking)](./algorithms/13.backtracking/README.md)
 14. [動態規劃 (Dynamic Programming)](./algorithms/14.dynamic-programming/README.md)
-15. 貪婪 (Greedy)
-16. 位元操作 (Bit Manipulation)
+15. [貪婪 (Greedy)](./algorithms/15.greedy/README.md)
+16. [位元操作 (Bit Manipulation)](./algorithms/16.bit-manipulation/README.md)
 
 ## Basic - LeetCode 75
 
@@ -470,7 +470,7 @@ Must-do List for Interview Prep
 
 | Backtracking                              |                |        |
 | ----------------------------------------- | -------------- | ------ |
-| 17. Letter Combinations of a Phone Number | Solution       | Medium |
+| 17. Letter Combinations of a Phone Number | [Solution][17] | Medium |
 | 77. Combinations                          | Solution       | Medium |
 | 46. Permutations                          | [Solution][46] | Medium |
 | 39. Combination Sum                       | Solution       | Medium |
@@ -478,6 +478,7 @@ Must-do List for Interview Prep
 | 22. Generate Parentheses                  | Solution       | Medium |
 | 79. Word Search                           | Solution       | Medium |
 
+[17]: ./src/page-1/17.%20Letter%20Combinations%20of%20a%20Phone%20Number/letterCombinations.ts
 [46]: ./src/page-1/46.%20Permutations/permute.ts
 
 | Divide & Conquer                                |                 |        |
diff --git a/algorithms/1.array/README.md b/algorithms/1.array/README.md
index efdd1e6..238e047 100644
--- a/algorithms/1.array/README.md
+++ b/algorithms/1.array/README.md
@@ -138,3 +138,39 @@ for (let i = k; i < nums.length; i++) {
 ```ts
 maxSum; // 此時 `maxSum` 為最大和
 ```
+
+## 矩陣 (Matrix)
+
+```ts
+const matrix = [
+  [1, 2, 3],
+  [4, 5, 6],
+  [7, 8, 9],
+];
+```
+
+問題：將矩陣的橫行 (Row) 和縱列 (Column) 互換
+
+取得矩陣 `rows` 和 `cols`：
+
+```ts
+const rows = matrix.length;
+const cols = matrix[0].length;
+```
+
+建立一個與原本矩陣橫行和縱列互換的空白新矩陣：
+
+```ts
+const newMatrix = Array.from({ length: cols }, () => Array(rows));
+```
+
+迴圈走訪原本矩陣的所有元素，將其分配到新矩陣上：
+
+```ts
+for (let r = 0; r < rows; r++) {
+  for (let c = 0; c < cols; c++) {
+    // 橫行和縱列互換
+    newMatrix[c][r] = matrix[r][c];
+  }
+}
+```
diff --git a/algorithms/15.greedy/README.md b/algorithms/15.greedy/README.md
index 8d98459..669c5ba 100644
--- a/algorithms/15.greedy/README.md
+++ b/algorithms/15.greedy/README.md
@@ -1,3 +1,41 @@
 # 貪婪 (Greedy)
 
 ## 分數背包問題 (Fractional Knapsack Problem)
+
+給定一個背包，背包的容量是有限的，你可以選擇將物品裝入背包。每個物品有一個重量和價值，但你可以選擇將物品切割，部分裝入背包。目標是最大化裝入背包中的物品的總價值。
+
+物品：
+
+```ts
+const items = [
+  { weight: 1, value: 5 },
+  { weight: 2, value: 11 },
+  { weight: 3, value: 15 },
+];
+```
+
+單位價值：計算每個物品的單位重量價值 (價值/重量)
+
+每個物品的編號 (`i`) 及其對應的重量和價值：
+
+|   i | weights[i - 1] | values[i - 1] | values[i - 1] / weights[i - 1] |
+| --: | -------------: | ------------: | -----------------------------: |
+|   1 |              1 |             5 |                              5 |
+|   2 |              2 |            11 |                            5.5 |
+|   3 |              3 |            15 |                              5 |
+
+```ts
+values[i - 1] / weights[i - 1];
+```
+
+單位價值高低：根據單位價值將物品按從高到低排序
+
+|   i | weights[i - 1] | values[i - 1] | values[i - 1] / weights[i - 1] |
+| --: | -------------: | ------------: | -----------------------------: |
+|   2 |              2 |            11 |                            5.5 |
+|   1 |              1 |             5 |                              5 |
+|   3 |              3 |            15 |                              5 |
+
+```ts
+items.sort((a, b) => b.value / b.weight - a.value / a.weight);
+```
diff --git a/algorithms/16.bit-manipulation/README.md b/algorithms/16.bit-manipulation/README.md
index 4d106c5..8ab4789 100644
--- a/algorithms/16.bit-manipulation/README.md
+++ b/algorithms/16.bit-manipulation/README.md
@@ -1 +1,26 @@
 # 位元操作 (Bit Manipulation)
+
+二進位制
+
+- 0001 -> 1
+- 0010 -> 2
+- 0011 -> 3
+- 0100 -> 4
+- 0101 -> 5
+- 0110 -> 6
+- 0111 -> 7
+- 1000 -> 8
+
+左移：
+
+```ts
+const x = 1; // 0001
+x << 2; // 0100 -> 4
+```
+
+右移：
+
+```ts
+const x = 4; // 0100
+x >> 2; // 0001 -> 1
+```
diff --git a/src/page-1/67. Add Binary/addBinary.ts b/src/page-1/67. Add Binary/addBinary.ts
index af74bf0..dc7c63b 100644
--- a/src/page-1/67. Add Binary/addBinary.ts	
+++ b/src/page-1/67. Add Binary/addBinary.ts	
@@ -4,5 +4,17 @@ type AddBinary = (a: string, b: string) => string;
  * Accepted
  */
 export const addBinary: AddBinary = (a, b) => {
-  return (BigInt(`0b${a}`) + BigInt(`0b${b}`)).toString(2);
+  let x = BigInt(`0b${a}`); // Convert binary string 'a' to BigInt
+  let y = BigInt(`0b${b}`); // Convert binary string 'b' to BigInt
+
+  let carry: bigint;
+
+  while (y !== BigInt(0)) {
+    // Repeat until there's no carry
+    carry = x & y; // Calculate the carry
+    x = x ^ y; // Sum the bits without carry
+    y = carry << BigInt(1); // Move the carry to the left
+  }
+
+  return x.toString(2); // Convert the final result back to a binary string
 };