Bitwise Programming

# CHAPTER 25

Bitwise Programming #

1. Introduction #

2. Learning Objectives #

• Understand binary representations of numbers.

• Use Bitwise AND (&), OR (|), XOR (^), and NOT (~).

• Use Left Shift (<<) and Right Shift (>>).

• Understand Bit Masking for setting, clearing, and toggling bits.

3. Binary Refresher #

4. Bitwise Operators #

#### 1. Bitwise AND (&) Compares bits. Returns 1 if BOTH bits are 1. Otherwise, returns 0.

// 5 = 0101
// 3 = 0011
// ---------
// & = 0001  (which is 1)
int result = 5 & 3; // result is 1

#### 2. Bitwise OR (|) Returns 1 if AT LEAST ONE bit is 1.

// 5 = 0101
// 3 = 0011
// ---------
// | = 0111  (which is 7)
int result = 5 | 3; // result is 7

#### 3. Bitwise XOR (^) - Exclusive OR Returns 1 if the bits are DIFFERENT. Returns 0 if they are the SAME.

// 5 = 0101
// 3 = 0011
// ---------
// ^ = 0110  (which is 6)
int result = 5 ^ 3; // result is 6

*(Fun Fact: XOR is used heavily in basic cryptography and for swapping two variables without a temporary variable!)*

#### 4. Bitwise NOT (~) - One's Complement Flips all 1s to 0s, and 0s to 1s.

// 5 = 0000 0101
// ~5 = 1111 1010  (which is -6 in 2's complement representation)
int result = ~5; 

5. Shift Operators #

// 5 = 0000 0101
// 5 << 1 = 0000 1010 (which is 10)
int result = 5 << 1; 

#### Right Shift (>>) Shifts bits to the right, discarding the rightmost bits. This is mathematically equivalent to dividing by 2.

// 10 = 0000 1010
// 10 >> 1 = 0000 0101 (which is 5)
int result = 10 >> 1; 

6. Bit Masking #

Assuming PORTA = 0000 0000:

• Setting a bit (turning it on): Use OR (|)

• Clearing a bit (turning it off): Use AND with NOT (& ~)

• Toggling a bit (flipping it): Use XOR (^)

7. Common Mistakes #

• Confusing Logical AND (&&) with Bitwise AND (&):

• Shifting negative numbers: Right shifting a negative integer invokes implementation-defined behavior in C (arithmetic vs logical shift).

8. Exercises #

1. 1. Write a program to check if a number is Even or Odd using the Bitwise AND operator. (Hint: num & 1).

1. 2. Write a program to multiply a number by 4 using the Left Shift operator.

1. 3. Write a program to swap two variables using the XOR (^) operator.

9. MCQ Quiz with Answers #

10. Interview Questions #

• Q: Write a C program to count the number of set bits (1s) in an integer using bitwise operators.

• Q: How do you check if a number is a power of 2 using bitwise operators? (Hint: (n & (n-1)) == 0).

• Q: Explain why left shift (<<) multiplies a number by 2.

11. Summary #

12. Next Chapter Recommendation #