added first exercise for bit manipulation

exercises/097_bit_manipulation.zig

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+// Bit manipulations is a very powerful tool just also from Zig.
+// Since the dawn of the computer age, numerous algorithms have been
+// developed that solve tasks solely by moving, setting, or logically
+// combining bits.
+//
+// Zig also uses direct bit manipulation in its standard library for
+// functions where possible. And it is often possible with calculations
+// based on integers.
+//
+// Often it is not easy to understand at first glance what exactly these
+// algorithms do when only "numbers" in memory areas change outwardly.
+// But it must never be forgotten that the numbers only represent the
+// interpretation of the bit sequences.
+//
+// Quasi the reversed case we have otherwise, namely that we represent
+// numbers in bit sequences.
+//
+// We remember: 1 byte = 8 bits = 11111111 = 255 decimal = FF hex.
+//
+// Zig provides all the necessary functions to change the bits inside
+// a variable. It is distinguished whether the bit change leads to an
+// overflow or not.The details are in the Zig documentation in section
+// 10.1 "Table of Operators".
+//
+// Here are some examples of how the bits of variables can be changed:
+//
+//          const numOne: u8 = 15;        //   =  0000 1111
+//          const numTwo: u8 = 245;       //   =  1111 0101
+//
+//          const res1 = numOne >> 4;     //   =  0000 0000 - shift right
+//          const res2 = numOne << 4;     //   =  1111 0000 - shift left
+//          const res3 = numOne & numTwo; //   =  0000 0101 - and
+//          const res4 = numOne | numTwo; //   =  1111 1111 - or
+//          const res5 = numOne ^ numTwo; //   =  1111 1010 - xor
+//
+//
+// To familiarize ourselves with bit manipulation, we start with a simple
+// but often underestimated function and then add other exercises in
+// loose order.
+//
+// The following text contains excerpts from Wikipedia.
+//
+// Swap
+// In computer programming, the act of swapping two variables refers to
+// mutually exchanging the values of the variables. Usually, this is
+// done with the data in memory. For example, in a program, two variables
+// may be defined thus (in pseudocode):
+//
+//                        data_item x := 1
+//                        data_item y := 0
+//
+//                        swap (x, y);
+//
+// After swap() is performed, x will contain the value 0 and y will
+// contain 1; their values have been exchanged. The simplest and probably
+// most widely used method to swap two variables is to use a third temporary
+// variable:
+//
+//                        define swap (x, y)
+//                        temp := x
+//                        x := y
+//                        y := temp
+//
+// However, with integers we can also achieve the swap function simply by
+// bit manipulation. To do this, the variables are mutually linked with xor
+// and the result is the same.
+
+const std = @import("std");
+const print = std.debug.print;
+
+pub fn main() !void {
+
+    // As in the example above, we use 1 and 0 as values for x and y
+    var x: u8 = 1;
+    var y: u8 = 0;
+
+    // Now we swap the values of the two variables by doing xor on them
+    x ^= y;
+    y ^= x;
+
+    // What must be written here?
+    ???;
+
+    print("x = {d}; y = {d}\n", .{ x, y });
+}
+
+// This variable swap takes advantage of the fact that the value resulting
+// from the xor of two values contains both of these values.
+// This circumstance was (and still is) sometimes used for encryption.
+// Value XOR Key = Crypto. => Crypto XOR Key = Value.
+// Since this can be swapped arbitrarily, you can swap two variables in this way.
+//
+// For Crypto it is better not to use this, but in sorting algorithms like
+// Bubble Sort it works very well.

patches/patches/097_bit_manipulation.patch

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+82c82
+<     ???;
+---
+>     x ^= y;