Bitmasks and Bit Manipulation
Work with individual bits! Set, clear, toggle, and check bits. Implement permission systems and flags efficiently.
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What You Will Learn
- ✓Understand binary representation
- ✓Set, clear, and toggle individual bits
- ✓Check if a bit is set
- ✓Implement permission flags
?Why Do We Need Bitmasks?
Imagine storing 8 yes/no settings. You could use 8 bool variables (8 bytes), or use 1 byte with bitmasks. Bitmasks are essential for:
File Permissions
chmod 755 uses octal bitmasks:
r-x = 101 = 5 (Group)
r-x = 101 = 5 (Others)
Game Development
Store player states, power-ups, collision layers — all in compact bit flags.
Hardware & Embedded
Control registers in microcontrollers are all bit fields.
Network Protocols
TCP/IP headers pack multiple flags into single bytes.
Memory savings: Storing 32 boolean flags takes 32 bytes with bool, but only 4 bytes with bitmasks — 8× more efficient!
01What are Bitmasks?
• Simple Definition
A bitmask is a pattern of bits used to manipulate individual bits within a number. Each bit acts as an ON/OFF flag!
Key Benefits
Memory Efficient
Store 8 flags in 1 byte!
Fast Operations
Bitwise ops are very fast
Permissions
Read, Write, Execute flags
Hardware Control
Control device registers
02Bitwise Operators Review
| Operator | Name | Description | Example |
|---|---|---|---|
| & | AND | 1 if both bits are 1 | 5 & 3 = 1 |
| | | OR | 1 if either bit is 1 | 5 | 3 = 7 |
| ^ | XOR | 1 if bits are different | 5 ^ 3 = 6 |
| ~ | NOT | Flip all bits | ~5 = -6 |
| << | Left Shift | Shift bits left | 5 << 1 = 10 |
| >> | Right Shift | Shift bits right | 5 >> 1 = 2 |
03Understanding Binary: Visual Guide
# 8-bit Number Visualization
Each bit position has a power-of-2 value. To get the decimal value, add up where bits are 1.
Example: 13 in binary
8 + 4 + 1 = 13
04Common Bitmask Operations
Visual: Set Bit 2 of value 9
Value: 9 = 0000 1001
Mask: 1 << 2 = 0000 0100
Result: 13 = 0000 1101
| Operation | Code | Description |
|---|---|---|
| Set bit | x | (1 << n) | Turn bit n ON (use OR with mask) |
| Clear bit | x & ~(1 << n) | Turn bit n OFF (AND with inverted mask) |
| Toggle bit | x ^ (1 << n) | Flip bit n (XOR toggles) |
| Check bit | (x >> n) & 1 | Is bit n set? (returns 0 or 1) |
1#include <stdio.h>23// Helper function to print binary4void printBinary(unsigned int n, int bits) {5 for (int i = bits - 1; i >= 0; i--) {6 printf("%d", (n >> i) & 1);7 }8}910int main() {11 unsigned int x = 0b00001010; // Start with 1012 13 printf("Original: ");14 printBinary(x, 8);15 printf(" = %d\n", x);16 17 // SET bit 0 (rightmost)18 x = x | (1 << 0);19 printf("Set bit 0: ");20 printBinary(x, 8);21 printf(" = %d\n", x);22 23 // SET bit 424 x = x | (1 << 4);25 printf("Set bit 4: ");26 printBinary(x, 8);27 printf(" = %d\n", x);28 29 // CLEAR bit 130 x = x & ~(1 << 1);31 printf("Clear bit 1: ");32 printBinary(x, 8);33 printf(" = %d\n", x);34 35 // TOGGLE bit 336 x = x ^ (1 << 3);37 printf("Toggle bit 3:");38 printBinary(x, 8);39 printf(" = %d\n", x);40 41 // CHECK if bit 4 is set42 if ((x >> 4) & 1) {43 printf("Bit 4 is SET\n");44 } else {45 printf("Bit 4 is NOT set\n");46 }47 48 return 0;49}Original: 00001010 = 10
Set bit 0: 00001011 = 11
Set bit 4: 00011011 = 27
Clear bit 1: 00011001 = 25
Toggle bit 3:00010001 = 17
Bit 4 is SET
04Practical Example: File Permissions
1#include <stdio.h>23// Define permission flags using bit positions4#define READ (1 << 0) // 001 = 15#define WRITE (1 << 1) // 010 = 26#define EXECUTE (1 << 2) // 100 = 478void printPermissions(int perms) {9 printf("Permissions: ");10 if (perms & READ) printf("Read ");11 if (perms & WRITE) printf("Write ");12 if (perms & EXECUTE) printf("Execute ");13 printf("\n");14}1516int main() {17 int permissions = 0; // No permissions18 19 printf("=== File Permission System ===\n\n");20 21 // Grant READ permission22 permissions |= READ;23 printf("After granting READ:\n");24 printPermissions(permissions);25 26 // Grant WRITE permission27 permissions |= WRITE;28 printf("After granting WRITE:\n");29 printPermissions(permissions);30 31 // Grant EXECUTE permission32 permissions |= EXECUTE;33 printf("After granting EXECUTE:\n");34 printPermissions(permissions);35 36 // Revoke WRITE permission37 permissions &= ~WRITE;38 printf("After revoking WRITE:\n");39 printPermissions(permissions);40 41 // Check specific permission42 if (permissions & EXECUTE) {43 printf("\nUser CAN execute this file.\n");44 }45 46 if (!(permissions & WRITE)) {47 printf("User CANNOT write to this file.\n");48 }49 50 // Grant multiple at once51 int fullAccess = READ | WRITE | EXECUTE;52 printf("\nFull access value: %d (binary: ", fullAccess);53 for (int i = 2; i >= 0; i--) printf("%d", (fullAccess >> i) & 1);54 printf(")\n");55 56 return 0;57}=== File Permission System ===
After granting READ:
Permissions: Read
After granting WRITE:
Permissions: Read Write
After granting EXECUTE:
Permissions: Read Write Execute
After revoking WRITE:
Permissions: Read Execute
User CAN execute this file.
User CANNOT write to this file.
Full access value: 7 (binary: 111)
05Practical Example: Game Flags
1#include <stdio.h>23// Game state flags4#define HAS_SWORD (1 << 0) // 00015#define HAS_SHIELD (1 << 1) // 00106#define HAS_POTION (1 << 2) // 01007#define QUEST_COMPLETE (1 << 3) // 100089void printInventory(int flags) {10 printf("Inventory: ");11 if (flags & HAS_SWORD) printf("[Sword] ");12 if (flags & HAS_SHIELD) printf("[Shield] ");13 if (flags & HAS_POTION) printf("[Potion] ");14 if (flags & QUEST_COMPLETE) printf("[Quest✓] ");15 if (flags == 0) printf("[Empty]");16 printf("\n");17}1819int main() {20 int playerFlags = 0;21 22 printf("=== Adventure Game ===\n\n");23 printInventory(playerFlags);24 25 // Pick up sword26 printf("You found a SWORD!\n");27 playerFlags |= HAS_SWORD;28 printInventory(playerFlags);29 30 // Pick up shield31 printf("You found a SHIELD!\n");32 playerFlags |= HAS_SHIELD;33 printInventory(playerFlags);34 35 // Use potion (can't - don't have one!)36 if (playerFlags & HAS_POTION) {37 printf("Used potion!\n");38 playerFlags &= ~HAS_POTION;39 } else {40 printf("No potion to use!\n");41 }42 43 // Pick up potion44 printf("You found a POTION!\n");45 playerFlags |= HAS_POTION;46 printInventory(playerFlags);47 48 // Complete quest49 printf("QUEST COMPLETE!\n");50 playerFlags |= QUEST_COMPLETE;51 printInventory(playerFlags);52 53 // Check if ready for boss (need sword AND shield)54 if ((playerFlags & HAS_SWORD) && (playerFlags & HAS_SHIELD)) {55 printf("\nYou are ready to fight the boss!\n");56 }57 58 return 0;59}=== Adventure Game ===
Inventory: [Empty]
You found a SWORD!
Inventory: [Sword]
You found a SHIELD!
Inventory: [Sword] [Shield]
No potion to use!
You found a POTION!
Inventory: [Sword] [Shield] [Potion]
QUEST COMPLETE!
Inventory: [Sword] [Shield] [Potion] [Quest✓]
You are ready to fight the boss!
!Code Pitfalls: Common Mistakes & What to Watch For
Common Mistakes with Bitmasks
Copying code often make subtle errors with bitwise operations:
- ✗Confusing & and &&: Code often uses logical AND when bitwise AND is needed, or vice versa
- ✗Precedence mistakes: Beginners often forget that == has higher precedence than &, writing
x & FLAG == 0 - ✗Wrong bit position: Beginners often count bits from wrong end or uses 1-based instead of 0-based indexing
- ✗Sign extension issues: Beginners often shift signed integers without considering sign bit behavior
Always Understand Before Using
Test bitmask operations with specific values and trace the binary. Use parentheses liberally: (x & FLAG) == 0 not x & FLAG == 0. Use unsigned types for shifting to avoid sign extension surprises.
07Frequently Asked Questions
Q:What are common bit manipulation patterns I should memorize?
A: Key patterns:x | mask sets bits,x & ~mask clears bits,x ^ mask toggles bits,x & mask tests bits,x & (x-1) clears lowest set bit,x & -x isolates lowest set bit. These patterns appear constantly in systems programming and interviews.
Q:Why use bitmasks instead of multiple booleans?
A: Memory efficiency! 8 booleans = 8 bytes; 8 flags in one byte. Plus you can pass all flags as a single integer, combine flags with OR, and test multiple conditions in one operation. Common in system APIs and embedded programming.
Q:How do I count the number of set bits?
A: This is called "popcount" (population count). Loop through and test each bit, or use GCC's builtin:__builtin_popcount(x). This is useful for counting active flags or in algorithms like Hamming distance.
Q:How do I find the lowest/highest set bit?
A: For lowest set bit:x & (-x) isolates it. For position, use__builtin_ctz(x) (count trailing zeros). For highest bit, use __builtin_clz(x) (count leading zeros). These are crucial for efficient bitboard algorithms and priority queues.
Q:What does 1 << n mean?
A: Left shift 1 by n positions, creating a number with only bit n set. 1 << 0 = 1,1 << 3 = 8 (binary 1000). This is how we create masks for individual bit positions.
Q:How do I combine multiple flags?
A: Use OR:READ | WRITE | EXECUTE combines all three. This is why you see function calls likeopen("file", O_RDWR | O_CREAT).
Q:How do I check if a number is a power of 2?
A: Use the expression(n > 0) && ((n & (n - 1)) == 0). Powers of 2 have exactly one bit set, so n & (n-1) clears that bit, giving 0. This is a classic bit manipulation trick used in allocators and hash tables.
Q:How do I swap two values without a temp variable?
A: XOR swap:a ^= b; b ^= a; a ^= b;This works because XOR is its own inverse. However, this is mainly a curiosity— modern compilers optimize regular swaps better, and XOR swap fails if a and b are the same variable.
Q:What's the ~ operator?
A: Bitwise NOT — flips all bits.~(1 << 3) = 11110111. Used to create masks for clearing bits: x & ~FLAG clears that flag while keeping all others.
Q:Where are bitmasks used in real programming?
A: File permissions (Unix), network packet headers, CPU flags, feature toggles, compression algorithms, graphics (color channels), game states, embedded systems, and low-level hardware control.
07Summary
Key Takeaways
- •Bitmask: Pattern of bits as flags
- •Set bit: x | (1 << n)
- •Clear bit: x & ~(1 << n)
- •Toggle bit: x ^ (1 << n)
- •Check bit: (x >> n) & 1
- •Use cases: Permissions, flags, hardware, games
- •Memory efficient: Store 8+ flags in one byte
- •Combine flags: Use OR to set multiple: READ | WRITE
- •Test flags: Use AND to check if a flag is set
- •Best practice: Define flags with meaningful names using #define or enum
08When to Use Bitmasks
Perfect for Compact Flag Storage
Use bitmasks when you have multiple boolean options that are often passed together, like file permissions or window styles. They're also ideal for hardware registers and protocols where every bit has meaning. Avoid them when code clarity matters more than memory—separate booleans are often easier to understand.
Test Your Knowledge
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