Bitwise Calculator

Bitwise operations work directly on the binary representation of numbers, manipulating individual bits. They are fundamental to low-level programming, cryptography, and many payment security operations.

Basic Bitwise Operations

• AND (&): Returns 1 if both corresponding bits are 1, otherwise 0. Used for masking and testing specific bits.
• OR (|): Returns 1 if at least one of the corresponding bits is 1, otherwise 0. Used for setting specific bits.
• XOR (^): Returns 1 if exactly one of the corresponding bits is 1, otherwise 0. Used in cryptography and for toggling bits.
• NOT (~): Inverts all bits, changing 1s to 0s and 0s to 1s. Used for creating bit masks and complements.
• Shift Left (<<): Moves all bits to the left by a specified number of positions. Equivalent to multiplying by powers of 2.
• Shift Right (>>): Moves all bits to the right by a specified number of positions. Equivalent to dividing by powers of 2.

Applications in Payment Security

• Cryptographic Operations: Many encryption algorithms use bitwise operations as fundamental building blocks.
• ISO 8583 Bitmaps: Bitwise operations are used to manipulate and interpret the bitmap fields that indicate which data elements are present in a message.
• EMV Processing: Terminal Verification Results (TVR) and other EMV data elements use bit flags to indicate various conditions.
• Key Derivation: Bitwise operations are used in key derivation functions for payment security.
• PIN Block Operations: XOR operations are fundamental to PIN block formats used in PIN security.

Number Formats

When working with bitwise operations, numbers can be represented in different formats:

• Binary: Base-2 representation using only 0s and 1s (e.g., 10101010)
• Hexadecimal: Base-16 representation using 0-9 and A-F (e.g., AA)
• Decimal: Base-10 representation using 0-9 (e.g., 170)

Converting between these formats is essential for bitwise operations, especially when working with payment protocols that specify fields in different formats.