diff --git a/README.md b/README.md
index 2e98d4d..843b515 100644
--- a/README.md
+++ b/README.md
@@ -93,6 +93,7 @@ The architectural choices, trade-offs, and design patterns for each algorithm ar
 * [ADR 0016: Bottom-Up Tabulation with Backtracking for 0/1 Knapsack](docs/adr/0016-use-bottom-up-tabulation-with-backtracking-for-01-knapsack.md)
 * [ADR 0017: Bottom-Up Tabulation with Diagonal Backtracking for LCS](docs/adr/0017-use-bottom-up-tabulation-with-diagonal-backtracking-for-lcs.md)
 * [ADR 0018: Binary Max-Heap for Heap Sort](docs/adr/0018-use-binary-max-heap-for-heap-sort.md)
+* [ADR 0019: Iterative Midpoint Bisection for Binary Search](docs/adr/0019-use-iterative-midpoint-bisection-for-binary-search.md)
 
 ---
 
@@ -122,4 +123,5 @@ To ensure uniformity, this repository follows strict standards derived from **PE
 14. **Bounded Traversal Footprint:** The Singly Linked List's `search`/`delete`/`reverse` operations are strictly O(n) iterative walks with no recursion, preventing stack-depth exhaustion on very large untrusted input lists.
 15. **Iterative DP, No Recursion Limits:** The 0/1 Knapsack solver uses bottom-up tabulation rather than top-down recursion, avoiding Python's `RecursionError` on large item counts.
 16. **Quadratic Complexity Awareness:** LCS runs in $O(n \times m)$ time and space; callers should bound input string lengths when comparing untrusted, attacker-controlled text to avoid excessive memory allocation on very large inputs.
-17. **In-Place Worst-Case Guarantee:** Heap Sort provides the same $O(n \log n)$ worst-case guarantee as Merge Sort but with $O(1)$ auxiliary space, useful when both adversarial-input resilience and memory constraints matter simultaneously.
\ No newline at end of file
+17. **In-Place Worst-Case Guarantee:** Heap Sort provides the same $O(n \log n)$ worst-case guarantee as Merge Sort but with $O(1)$ auxiliary space, useful when both adversarial-input resilience and memory constraints matter simultaneously.
+18. **Precondition Responsibility:** Binary Search assumes sorted input and does not validate it; callers must guarantee sortedness themselves, since verifying it would negate the algorithm's logarithmic performance advantage.
\ No newline at end of file
diff --git a/ROADMAP.md b/ROADMAP.md
index 46d8bf9..198f995 100644
--- a/ROADMAP.md
+++ b/ROADMAP.md
@@ -38,6 +38,16 @@ This document serves as the long-term architectural roadmap for this learning re
 *   **Heap Sort**: In-place comparison sort built atop a binary max-heap, contrasting Quicksort/Merge Sort's partitioning and merging strategies. (Completed)
 *   **Euclidean Algorithm (GCD)**: Iterative remainder-based reduction resolving the greatest common divisor between two integers.
 *   **Valid Parentheses (Stack-Based Matching)**: Stack-tracked bracket balancing validating correctly nested and closed symbol pairs.
+*   **Binary Search**: Divide-and-conquer $O(\log n)$ lookup resolving a target's position within a sorted array. (Completed)
+
+### Phase 7: Graph Traversal & Minimum Spanning Trees
+*   **Breadth-First Search (BFS)**: Queue-driven level-order graph traversal resolving shortest unweighted paths and reachability.
+*   **Depth-First Search (DFS)**: Stack/recursion-driven graph traversal resolving connectivity, cycle detection, and ordering.
+*   **Kruskal's Algorithm**: Greedy edge-sorted minimum spanning tree construction built atop the existing Union-Find structure.
+
+### Phase 8: Numerical Methods & Ranking Algorithms
+*   **PageRank (Power Iteration)**: Iterative eigenvector approximation ranking nodes by weighted incoming link importance.
+*   **Fast Inverse Square Root**: Bit-level floating-point approximation technique accelerating $1/\sqrt{x}$ via a single Newton-Raphson refinement step.
 
 ---
 
diff --git a/docs/adr/0019-use-iterative-midpoint-bisection-for-binary-search.md b/docs/adr/0019-use-iterative-midpoint-bisection-for-binary-search.md
new file mode 100644
index 0000000..6161db0
--- /dev/null
+++ b/docs/adr/0019-use-iterative-midpoint-bisection-for-binary-search.md
@@ -0,0 +1,10 @@
+# 19. Use Iterative Midpoint Bisection for Binary Search
+
+* **Status:** Approved
+* **Context:** Phase 6 required a foundational $O(\log n)$ lookup mechanism as a baseline searching primitive, applicable whenever data is already sorted (as opposed to linear O(n) scanning).
+* **Decision:** We implemented **Binary Search** iteratively, using `low + (high - low) // 2` to compute the midpoint (rather than `(low + high) // 2`) and narrowing the search window each iteration based on comparison against the target.
+* **Consequences:**
+  * Achieves $O(\log n)$ time and $O(1)$ space, since the iterative approach avoids any recursive call-stack growth.
+  * The `low + (high - low) // 2` midpoint formula is a defensive habit carried over from languages with fixed-width integers (where `low + high` can overflow); it is unnecessary in Python's arbitrary-precision integers but costs nothing and keeps the implementation portable as a reference pattern.
+  * *Trade-off:* The function assumes its input is already sorted and provides no validation of that precondition — enforcing sortedness would cost an extra $O(n)$ pass, defeating the purpose of using binary search in the first place. Callers are responsible for ensuring sorted input.
+
diff --git a/service/http_app.py b/service/http_app.py
index e8cdb21..c061d44 100644
--- a/service/http_app.py
+++ b/service/http_app.py
@@ -31,6 +31,11 @@ class SortRequest(BaseModel):
     values: List[int]
 
 
+class BinarySearchRequest(BaseModel):
+    sorted_values: List[int]
+    target: int
+
+
 class KmpSearchRequest(BaseModel):
     text: str
     pattern: str
@@ -122,6 +127,12 @@ def sort_heap_sort(request: SortRequest) -> List[int]:
     return _call(tools.sort_heap_sort, request.values)
 
 
+@app.post("/searching/binary-search")
+def search_binary_search(request: BinarySearchRequest) -> Dict:
+    """Returns the index of a target within a sorted array, or -1 if absent."""
+    return _call(tools.search_binary_search, request.sorted_values, request.target)
+
+
 @app.post("/string-matching/kmp")
 def search_kmp(request: KmpSearchRequest) -> List[int]:
     """Finds every 0-indexed starting position of a pattern within a text."""
diff --git a/service/mcp_server.py b/service/mcp_server.py
index 5359051..1c5988e 100644
--- a/service/mcp_server.py
+++ b/service/mcp_server.py
@@ -39,6 +39,12 @@ def sort_heap_sort(values: List[int]) -> List[int]:
     return tools.sort_heap_sort(values)
 
 
+@mcp.tool()
+def search_binary_search(sorted_values: List[int], target: int) -> Dict:
+    """Returns the index of `target` within a sorted array, or -1 if absent."""
+    return tools.search_binary_search(sorted_values, target)
+
+
 @mcp.tool()
 def search_kmp(text: str, pattern: str) -> List[int]:
     """Finds every 0-indexed starting position of `pattern` within `text`."""
diff --git a/service/tools.py b/service/tools.py
index 4e7efa5..74102c8 100644
--- a/service/tools.py
+++ b/service/tools.py
@@ -26,6 +26,7 @@
 from src.machine_learning.kmeans import KMeans
 from src.machine_learning.pca import PCA
 from src.numeric.sieve import sieve_of_eratosthenes
+from src.searching.binary_search import binary_search
 from src.sorting.heap_sort import heap_sort
 from src.sorting.merge_sort import merge_sort
 from src.sorting.quicksort import quicksort
@@ -59,6 +60,11 @@ def sort_heap_sort(values: List[int]) -> List[int]:
     return heap_sort(values)
 
 
+def search_binary_search(sorted_values: List[int], target: int) -> Dict:
+    """Returns the index of `target` within a sorted array, or -1 if absent."""
+    return {"index": binary_search(sorted_values, target)}
+
+
 def search_kmp(text: str, pattern: str) -> List[int]:
     """Finds every 0-indexed starting position of `pattern` within `text`."""
     return kmp_search(text, pattern)
diff --git a/src/searching/__init__.py b/src/searching/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/src/searching/binary_search.py b/src/searching/binary_search.py
new file mode 100644
index 0000000..6217a6f
--- /dev/null
+++ b/src/searching/binary_search.py
@@ -0,0 +1,29 @@
+"""Binary Search module implementing iterative divide-and-conquer lookups on sorted arrays."""
+
+from typing import List
+
+
+def binary_search(sorted_array: List[int], target: int) -> int:
+    """Returns the index of `target` within a sorted array, or -1 if absent.
+
+    The input array must already be sorted in ascending order; behavior on an
+    unsorted array is undefined.
+
+    Complexity Analysis:
+        Time Complexity: O(log n) where n = len(sorted_array).
+        Space Complexity: O(1) — iterative, no recursive call stack growth.
+    """
+    low, high = 0, len(sorted_array) - 1
+
+    while low <= high:
+        # Midpoint computed this way avoids integer overflow in lower-level languages
+        mid = low + (high - low) // 2
+
+        if sorted_array[mid] == target:
+            return mid
+        if sorted_array[mid] < target:
+            low = mid + 1
+        else:
+            high = mid - 1
+
+    return -1
diff --git a/tests/test_searching.py b/tests/test_searching.py
new file mode 100644
index 0000000..0bc9588
--- /dev/null
+++ b/tests/test_searching.py
@@ -0,0 +1,32 @@
+"""Comprehensive evaluation suite tracking Binary Search lookup operations."""
+
+from src.searching.binary_search import binary_search
+
+
+def test_binary_search_finds_present_values():
+    """Verifies correct index resolution across first, middle, and last positions."""
+    sorted_array = [1, 3, 5, 7, 9, 11, 13]
+
+    assert binary_search(sorted_array, 1) == 0
+    assert binary_search(sorted_array, 7) == 3
+    assert binary_search(sorted_array, 13) == 6
+
+
+def test_binary_search_absent_value_returns_negative_one():
+    """Ensures a target not present in the array resolves to -1."""
+    sorted_array = [2, 4, 6, 8, 10]
+
+    assert binary_search(sorted_array, 5) == -1
+    assert binary_search(sorted_array, -1) == -1
+    assert binary_search(sorted_array, 100) == -1
+
+
+def test_binary_search_empty_array():
+    """Ensures searching an empty array returns -1 without error."""
+    assert binary_search([], 5) == -1
+
+
+def test_binary_search_single_element_array():
+    """Ensures single-element arrays resolve correctly for both match and mismatch."""
+    assert binary_search([42], 42) == 0
+    assert binary_search([42], 7) == -1
diff --git a/tests/test_service_http_app.py b/tests/test_service_http_app.py
index a9f240c..249ea02 100644
--- a/tests/test_service_http_app.py
+++ b/tests/test_service_http_app.py
@@ -28,6 +28,23 @@ def test_http_sort_heap_sort():
     assert response.json() == [1, 2, 3, 4, 5]
 
 
+def test_http_search_binary_search():
+    """Verifies the Binary Search endpoint returns the correct index, or -1 if absent."""
+    response = client.post(
+        "/searching/binary-search",
+        json={"sorted_values": [1, 3, 5, 7, 9], "target": 7},
+    )
+    assert response.status_code == 200
+    assert response.json() == {"index": 3}
+
+    response = client.post(
+        "/searching/binary-search",
+        json={"sorted_values": [1, 3, 5, 7, 9], "target": 4},
+    )
+    assert response.status_code == 200
+    assert response.json() == {"index": -1}
+
+
 def test_http_search_kmp():
     """Verifies the KMP search endpoint returns matching start indices."""
     response = client.post(
diff --git a/tests/test_service_mcp_server.py b/tests/test_service_mcp_server.py
index 7cc6b5c..6f9f268 100644
--- a/tests/test_service_mcp_server.py
+++ b/tests/test_service_mcp_server.py
@@ -18,6 +18,7 @@ def test_mcp_tool_registry_contains_all_algorithms():
         "sort_quicksort",
         "sort_merge_sort",
         "sort_heap_sort",
+        "search_binary_search",
         "search_kmp",
         "build_and_query_bst",
         "build_and_query_avl_tree",
@@ -52,6 +53,12 @@ def test_mcp_sort_heap_sort():
     assert mcp_server.sort_heap_sort([5, 2, 4, 1, 3]) == [1, 2, 3, 4, 5]
 
 
+def test_mcp_search_binary_search():
+    """Verifies the Binary Search tool returns the correct index, or -1 if absent."""
+    assert mcp_server.search_binary_search([1, 3, 5, 7, 9], target=7) == {"index": 3}
+    assert mcp_server.search_binary_search([1, 3, 5, 7, 9], target=4) == {"index": -1}
+
+
 def test_mcp_search_kmp():
     """Verifies the KMP search tool returns matching start indices."""
     assert mcp_server.search_kmp("ababcababc", "abc") == [2, 7]
diff --git a/tests/test_service_tools.py b/tests/test_service_tools.py
index e7f334b..20e5c40 100644
--- a/tests/test_service_tools.py
+++ b/tests/test_service_tools.py
@@ -20,6 +20,12 @@ def test_sort_heap_sort():
     assert tools.sort_heap_sort([5, 2, 4, 1, 3]) == [1, 2, 3, 4, 5]
 
 
+def test_search_binary_search():
+    """Verifies Binary Search wrapper returns the correct index, or -1 if absent."""
+    assert tools.search_binary_search([1, 3, 5, 7, 9], target=7) == {"index": 3}
+    assert tools.search_binary_search([1, 3, 5, 7, 9], target=4) == {"index": -1}
+
+
 def test_search_kmp():
     """Verifies KMP wrapper returns matching start indices."""
     assert tools.search_kmp("ababcababc", "abc") == [2, 7]