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Bitwise AND Operation

The AND operation compares two numbers bit-by-bit, returning 1 only when both input bits are 1. It's fundamental for bit masking, subnet masks, and flag checking in computing.

Concept Fundamentals
4
Truth Table Rows
64
Max Bits
3
Formats
1
CPU Cycles

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IP subnet masks use AND to extract network addresses from host IPs. value & (1 << n) checks if bit n is set — the fastest parity test. AND with 0 clears bits; AND with 1 preserves them.

Key quantities
4
Truth Table Rows
Key relation
64
Max Bits
Key relation
3
Formats
Key relation
1
CPU Cycles
Key relation

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Why: AND is used in networking (subnet masks), file permissions (Unix rwx), and hardware design (logic gates).

How: Compare each bit position: if both inputs are 1, output 1; otherwise output 0.

IP subnet masks use AND to extract network addresses from host IPs.value & (1 << n) checks if bit n is set — the fastest parity test.
Sources:MDN Bitwise ANDRFC 791 - IP Subnetting

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Start CalculatingEnter two values in binary, decimal, or hex to perform bitwise AND
∧

AND Operation — Bitwise Masking & Filtering

Compare bits, extract masks, check flags. Binary, decimal, hex.

📌 Examples — Click to Load

For educational and informational purposes only. Verify with a qualified professional.

🧮 Fascinating Math Facts

🔒

Unix file permissions use AND: 0644 & 0444 checks read permission for all.

— POSIX

🌐

192.168.1.5 & 255.255.255.0 = 192.168.1.0 (network address).

— RFC 791

📋 Key Takeaways

  • • AND truth table: 1 & 1 = 1; all other combinations = 0
  • • Masking: Use AND with 1s to extract bits, 0s to clear them
  • • Filtering: AND isolates specific bit positions (e.g., subnet masks)

💡 Did You Know?

🌐IP subnet masks use AND to extract network addresses — 192.168.1.5 & 255.255.255.0 = 192.168.1.0Source: RFC 791
⚡CPU ALUs perform AND in a single clock cycle — one of the fastest operations in hardwareSource: Computer Architecture
🖼️Image processing uses AND for masking, alpha blending, and bit-plane extractionSource: Graphics Programming
🔒Unix file permissions (rwx) use AND to check if a specific permission bit is setSource: POSIX
🔧Hardware design uses AND gates as fundamental building blocks in logic circuitsSource: Digital Logic
📦Data compression uses AND for bit packing and unpacking in binary formatsSource: Data Structures

📖 How AND Works

The bitwise AND operation compares two numbers bit by bit. For each position, the result is 1 only if both inputs are 1; otherwise it is 0. This makes AND ideal for masking (extracting or clearing specific bits) and filtering (e.g., checking flags, subnet masks).

Truth Table

ABA AND B
000
010
100
111

🎯 Expert Tips

Subnet masks

Use 255.255.255.0 (or /24) to extract network from IP. Host bits become 0.

Flag checking

value & (1 << n) checks if bit n is set. Non-zero = set.

Even/odd

n & 1 === 0 means even; n & 1 === 1 means odd. Fastest parity check.

Clear lower bits

Use mask with 1s in upper bits: 0xFFF0 clears lowest 4 bits.

⚖️ AND vs OR vs XOR

OperationUse Case1 & 11 & 0
ANDMasking, filtering10
ORSetting bits11
XORToggling, parity01

❓ Frequently Asked Questions

What is the difference between logical AND (&&) and bitwise AND (&)?

Logical AND returns true/false for boolean expressions. Bitwise AND operates on each bit of two integers and returns an integer. Use && for conditions; use & for bit manipulation.

How do I check if a specific bit is set using AND?

Use value & (1 << n). If the result is non-zero, bit n is set. Example: 13 & 4 checks if bit 2 is set (13 = 1101, 4 = 0100, result = 4 = set).

How is AND used in IP subnet masking?

The subnet mask has 1s for network bits and 0s for host bits. IP & mask = network address. 192.168.1.5 & 255.255.255.0 = 192.168.1.0.

Can AND be used for even/odd detection?

Yes. n & 1 extracts the LSB. Even numbers have LSB=0, odd have LSB=1. (n & 1) === 0 means even.

What is bit masking with AND?

A mask with 1s keeps those bits, 0s clear them. 0b10111010 & 0b00001111 keeps lower 4 bits, clears upper 4.

How does AND relate to Unix file permissions?

Permissions are octal: r=4, w=2, x=1. 0644 & 0444 checks read permission for all; result 0444 means read is set.

Why use AND instead of division for bit extraction?

AND is a single CPU instruction; division is slower. AND also avoids floating-point and works on unsigned integers.

What happens with different bit lengths in AND?

Shorter values are zero-extended. 8-bit 0xFF & 16-bit 0x0F0F = 0x000F (lower byte AND).

📊 Bitwise AND by the Numbers

1
Clock cycle (typical)
4
Truth table rows
64
Max bits supported
3
Formats (bin/dec/hex)

⚠️ Disclaimer: This calculator is for educational and programming reference. Bitwise operations assume unsigned integers. For signed integers, behavior may differ by language. Verify results in your target environment.

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