Bitwise Operations

systems math Bitwise Operations allow you to manipulate individual bits within a byte or word. These operators map directly to the Logic Gates (AND, OR, XOR) inside the CPU’s ALU. In Systems and Embedded programming, this is how you interact with hardware registers.

---

The Operators

Operator	Name	Function	Example (A=5 0101, B=3 0011)
&	AND	1 if both bits are 1.	A & B = 0001 (1)
|	OR	1 if either bit is 1.	A | B = 0111 (7)
^	XOR	1 if bits are different.	A ^ B = 0110 (6)
~	NOT	Inverts all bits (One’s Complement).	~A = 1010 (unsigned 4-bit)
<<	Left Shift	Shifts bits left (Multiply by $2^n$).	A << 1 = 1010 (10)
>>	Right Shift	Shifts bits right (Divide by $2^n$).	A >> 1 = 0010 (2)

---

Bitmasking Techniques

Controlling specific bits without affecting others (e.g., turning on an LED connected to Pin 5).

1. Setting a Bit (Turn ON) Use OR (|) with a mask.

// Turn on the 3rd bit (index 2)
x = x | (1 << 2);

2. Clearing a Bit (Turn OFF) Use AND (&) with the NOT (~) of the mask.

// Turn off the 3rd bit
x = x & ~(1 << 2);

3. Toggling a Bit (Flip) Use XOR (^) with a mask.

// Flip the 3rd bit
x = x ^ (1 << 2);

4. Checking a Bit Use AND (&).

if (x & (1 << 2)) {
    // 3rd bit is set
}

---