5. bit manipulation readme v2

05. Bit manipulation/README.md

@@ -26,4 +26,76 @@ The sign bit is kept, and all bits (sign bit too) are shifted.
 * -75: **1**0110101
 * -38: **1**1011010
 
+```c++
+int repeatedArithmeticShift(int x, int count) {
+    for (int i = 0; i < count; i++) {
+        x >>= 1; // Arithmetic shift by 1
+    }
+}
+
+int repeatedLogicalShift(int x, int count) {
+    for (int i = 0; i < count; i++) {
+        x >>>= 1; // Logical shift by 1
+    }
+}
+```
+
 ## 5.3. Common bit tasks: getting and setting
+
+### Get bit
+
+This method shifts 1 over by i bits, creating a value that looks like 00010000. By performing an AND with `num`, we clear all bits other than the bit at bit `i`. Then we compare it to 0. If the new value isn't 0, then bit i must have a 1. Otherwise, bit i is a 0.
+
+```c++
+boolean getBit(int num, int i) {
+    return ((num & (1 << i)) != 0);
+}
+```
+
+### Set bit
+
+This function shifts 1 over by i bits, creating a value like 00010000. By performing an OR with `num`, only the value at bit i will change. All other bits of the mask are zero, and won't affect `num`.
+
+```c++
+boolean setBit(int num, int i) {
+    return num | (1 << i);
+}
+```
+
+### Clear bit
+
+This is the opposite of `setBit`. We first create a number like 11101111. Then, we AND it with `num`. This clears the bit i and leaves the rest unchanged.
+
+```c++
+boolean clearBit(int num, int i) {
+    return num & ~(1 << i);
+}
+```
+
+To clear all bits from the most significant bit through i (inclusive), we create a mask with a 1 at the ith bit (1 << i). Then we substract 1 from it, giving us a sequence of zeros followed by i ones. We AND `num` with this mask, to leave just the last i bits.
+
+```c++
+boolean clearBitMSBthroughI(int num, int i) {
+    return num & ((1 << i) - 1);
+}
+```
+
+To clear all bits from i through 0 (inclusive), we take a sequence of all ones (which represents -1) and shift it left by i+1 bits. This gives a sequence of ones followed by i+1 zeros.
+
+```c++
+boolean clearBitIthrough0(int num, int i) {
+    return num & (-1 << (i+1));
+}
+```
+
+### Update bit
+
+To set the ith bit to a value v, we first clear the bit at position i, then we shift the value v, left by i bits. This will create a number with bit i equal to v and all other bits equal to 0. Finally, we OR these 2 numbers, updating the ith bit if v=1 and leaving it as 0 otherwise.
+
+```c++
+boolean updateBit(int num, int i, boolean bitIs1) {
+    int value = bitIs1 ? 1 : 0;
+    int mask = ~(1 << i);
+    return (num & mask) | (value << i);
+}
+```