Finished chapter 2

ch_02/exercise_02-09/main.c

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+/*
+ *
+ * Exercise 2-9. In a two's complement number system, x &= (x-1) deletes the
+ * rightmost 1-bit in x. Explain why. Use this observation to write a faster
+ * version of bitcount.
+ * rotated to the right by n positions.
+ *
+ * Observation:
+ * In a two's complement number system, x &= (x-1) deletes the rightmost
+ * 1-bit in x. The reason for that is simple once things are broken down.
+ * Using an example, let's say x is 19. 19 in binary is 10011.
+ * (x-1) is 18 or 10010 in binary. Using the bitwise AND operator the result
+ * is:
+ *   10011
+ * & 10010
+ * -------
+ *   10010
+ *
+ * 10010 is 18 and 10011 with the rightmost bit removed.
+ *
+ * Author: Kun Deng
+ */
+
+
+#include <stdio.h>
+#include <stdlib.h>
+
+
+// Counts the number of 1-bits in a number
+int bitcount(unsigned int x);
+
+// Counts the number of 1-bits in a number but faster than bitcount()
+int bitcount_improved(unsigned int x);
+
+
+int main(int argc, char **argv)
+{
+    unsigned int x = 511;
+
+    if (argc == 2)
+    {
+        x = atoi(argv[1]);
+    }
+
+    int bit_amount = bitcount(x);
+
+    printf("%d has %d bits\n", x, bit_amount);
+
+    int bit_amount_improved = bitcount_improved(x);
+
+    printf("%d has %d bits - Improved\n", x, bit_amount_improved);
+
+    return 0;
+}
+
+
+int bitcount(unsigned int x)
+{
+    int b;
+
+    for (b = 0; x != 0; x>>= 1)
+    {
+        if (x & 01)
+        {
+            ++b;
+        }
+    }
+
+    return b;
+}
+
+int bitcount_improved(unsigned int x)
+{
+    int b;
+
+    // x &= (x-1) is always removing the rightmost bit. With this it's easier
+    // to count the amount of 1-bits simply by incrementing b.
+    for (b = 0; x != 0; x &= (x-1))
+    {
+        ++b;
+    }
+
+    return b;
+}