Add FirstDifferentBit algorithm (#5866)

Author: Hardvan

DIRECTORY.md

@@ -31,6 +31,7 @@
             * [CountLeadingZeros](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/CountLeadingZeros.java)
             * [CountSetBits](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/CountSetBits.java)
             * [FindNthBit](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/FindNthBit.java)
+            * [FirstDifferentBit](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/FirstDifferentBit.java)
             * [GrayCodeConversion](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/GrayCodeConversion.java)
             * [HammingDistance](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/HammingDistance.java)
             * [HigherLowerPowerOfTwo](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/HigherLowerPowerOfTwo.java)
@@ -727,6 +728,7 @@
             * [CountLeadingZerosTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/CountLeadingZerosTest.java)
             * [CountSetBitsTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/CountSetBitsTest.java)
             * [FindNthBitTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/FindNthBitTest.java)
+            * [FirstDifferentBitTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/FirstDifferentBitTest.java)
             * [GrayCodeConversionTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/GrayCodeConversionTest.java)
             * [HammingDistanceTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/HammingDistanceTest.java)
             * [HigherLowerPowerOfTwoTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/HigherLowerPowerOfTwoTest.java)

src/main/java/com/thealgorithms/bitmanipulation/FirstDifferentBit.java

@@ -0,0 +1,33 @@
+package com.thealgorithms.bitmanipulation;
+
+/**
+ * This class provides a method to find the first differing bit
+ * between two integers.
+ *
+ * Example:
+ *  x = 10 (1010 in binary)
+ *  y = 12 (1100 in binary)
+ *  The first differing bit is at index 1 (0-based)
+ *  So, the output will be 1
+ *
+ * @author Hardvan
+ */
+public final class FirstDifferentBit {
+    private FirstDifferentBit() {
+    }
+
+    /**
+     * Identifies the index of the first differing bit between two integers.
+     * Steps:
+     * 1. XOR the two integers to get the differing bits
+     * 2. Find the index of the first set bit in XOR result
+     *
+     * @param x the first integer
+     * @param y the second integer
+     * @return the index of the first differing bit (0-based)
+     */
+    public static int firstDifferentBit(int x, int y) {
+        int diff = x ^ y;
+        return Integer.numberOfTrailingZeros(diff);
+    }
+}

src/test/java/com/thealgorithms/bitmanipulation/FirstDifferentBitTest.java

@@ -0,0 +1,15 @@
+package com.thealgorithms.bitmanipulation;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import org.junit.jupiter.params.ParameterizedTest;
+import org.junit.jupiter.params.provider.CsvSource;
+
+public class FirstDifferentBitTest {
+
+    @ParameterizedTest
+    @CsvSource({"10, 8, 1", "7, 5, 1", "15, 14, 0", "1, 2, 0"})
+    void testFirstDifferentBit(int x, int y, int expected) {
+        assertEquals(expected, FirstDifferentBit.firstDifferentBit(x, y));
+    }
+}