Bit Manipulation Basics AND OR XOR NOT Left Right Shift in DSA C

Mental Model

Bit manipulation changes numbers by flipping or moving their tiny on/off switches called bits.

Analogy: Imagine a row of light switches where each switch can be on or off. Bit operations flip, combine, or shift these switches to get new patterns.

Number 13 in bits (8 bits):
0 0 0 0 1 1 0 1
↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑
7 6 5 4 3 2 1 0 (bit positions)

Dry Run Walkthrough

Input: numbers: a = 13 (00001101), b = 10 (00001010)

Goal: Show results of AND, OR, XOR, NOT, left shift, and right shift on a and b

Step 1: Calculate a AND b

a = 00001101
b = 00001010
a AND b = 00001000 (8)

Why: AND keeps bits on only if both a and b have them on

Step 2: Calculate a OR b

a = 00001101
b = 00001010
a OR b = 00001111 (15)

Why: OR turns bits on if either a or b has them on

Step 3: Calculate a XOR b

a = 00001101
b = 00001010
a XOR b = 00000111 (7)

Why: XOR turns bits on only if a and b differ at that bit

Step 4: Calculate NOT a (invert bits)

a = 00001101
NOT a = 11110010 (242)

Why: NOT flips every bit from on to off or off to on

Step 5: Left shift a by 1 (multiply by 2)

a = 00001101
Left shift by 1 = 00011010 (26)

Why: Left shift moves bits left, adding a zero on right, doubling the number

Step 6: Right shift a by 2 (divide by 4)

a = 00001101
Right shift by 2 = 00000011 (3)

Why: Right shift moves bits right, dropping bits on right, dividing the number

Result:

Final results:
AND: 8 (00001000)
OR: 15 (00001111)
XOR: 7 (00000111)
NOT a: 242 (11110010)
Left shift a by 1: 26 (00011010)
Right shift a by 2: 3 (00000011)

Annotated Code

DSA C

#include <stdio.h>
#include <stdint.h>

void print_bits(uint8_t n) {
    for (int i = 7; i >= 0; i--) {
        printf("%d", (n >> i) & 1);
    }
}

int main() {
    uint8_t a = 13; // 00001101
    uint8_t b = 10; // 00001010

    uint8_t and_result = a & b; // bitwise AND
    uint8_t or_result = a | b;  // bitwise OR
    uint8_t xor_result = a ^ b; // bitwise XOR
    uint8_t not_result = ~a;    // bitwise NOT
    uint8_t left_shift = a << 1; // left shift by 1
    uint8_t right_shift = a >> 2; // right shift by 2

    printf("a = "); print_bits(a); printf(" (%d)\n", a);
    printf("b = "); print_bits(b); printf(" (%d)\n", b);

    printf("a AND b = "); print_bits(and_result); printf(" (%d)\n", and_result);
    printf("a OR b = "); print_bits(or_result); printf(" (%d)\n", or_result);
    printf("a XOR b = "); print_bits(xor_result); printf(" (%d)\n", xor_result);
    printf("NOT a = "); print_bits(not_result); printf(" (%d)\n", not_result);
    printf("a << 1 = "); print_bits(left_shift); printf(" (%d)\n", left_shift);
    printf("a >> 2 = "); print_bits(right_shift); printf(" (%d)\n", right_shift);

    return 0;
}

uint8_t and_result = a & b;

compute bitwise AND to keep bits on only if both a and b have them on

uint8_t or_result = a | b;

compute bitwise OR to turn bits on if either a or b has them on

uint8_t xor_result = a ^ b;

compute bitwise XOR to turn bits on only if bits differ

uint8_t not_result = ~a;

compute bitwise NOT to flip every bit

uint8_t left_shift = a << 1;

left shift bits by 1 to multiply by 2

uint8_t right_shift = a >> 2;

right shift bits by 2 to divide by 4

Output

a = 00001101 (13)

b = 00001010 (10)

a AND b = 00001000 (8)

a OR b = 00001111 (15)

a XOR b = 00000111 (7)

NOT a = 11110010 (242)

a << 1 = 00011010 (26)

a >> 2 = 00000011 (3)

Complexity Analysis

Time: O(1) because bitwise operations work on fixed-size bits directly

Space: O(1) because only a few variables are used regardless of input size

vs Alternative: Bit manipulation is much faster and uses less memory than arithmetic operations for these tasks

Edge Cases

a = 0 (all bits off)

AND, OR, XOR with any number behave as expected; NOT flips all bits to 1

DSA C

uint8_t not_result = ~a;

left shift causes bits to overflow beyond 8 bits

bits shifted out are lost, result wraps around in 8 bits

DSA C

uint8_t left_shift = a << 1;

right shift on zero

result remains zero as bits shifted in are zeros

DSA C

uint8_t right_shift = a >> 2;

When to Use This Pattern

When you need to quickly check, flip, or move individual bits in numbers, use bit manipulation because it is fast and memory efficient.

Common Mistakes

Mistake: Using signed integers for bit shifts causing unexpected sign extension
Fix: Use unsigned integers like uint8_t to avoid sign issues

Mistake: Confusing left shift with multiplication without considering overflow
Fix: Remember left shift can lose bits if they move beyond the fixed size

Summary

Bit manipulation changes numbers by flipping or moving their bits using AND, OR, XOR, NOT, and shifts.

Use it when you want fast, low-level control over individual bits in numbers.

Think of bits as tiny switches you can combine or move to get new numbers quickly.