# XYHASH

### Overview

XYXYX introduces a built-in hash function called XYHASH, which provides uniqueness to each XYXYX visual output.

XYHASH, instead of using numbers and characters to create an encoded hash, employs Hex colors as output. Simple and robust, the input that generates each XYHASH is the `tokenId`

of each XYXYX. For each combination of numbers that represents a `tokenId`

, an one-of-a-kind combination of two Hex colors is produced by the XYXYX contract.

### Uniqueness

The XYHASH function guarantees the uniqueness of each 1 full XYXYX by generating distinct hashes for every token. This ensures that no two XYXYX will ever duplicate. By capitalizing on the ERC-404's inherent characteristic of non-repeating token IDs, XYHASH uses each `tokenId`

as the input to create a unique output.

This method leverages the non-rollup feature of token IDs within the ERC-404, ensuring that each 1 full XYXYX retains a one-of-a-kind identity through a specifically generated hash, thereby maintaining the uniqueness of each token.

### XYHASH

Unlike traditional hash functions that output a string of numbers and characters, XYHASH generates outputs in the form of Hex color codes. This method is both straightforward and effective, utilizing the `tokenId`

of each XYXYX as the input variable.

Consequently, for every unique `tokenId`

, the XYXYX contract produces a specific pair of Hex colors. This mechanism ensures that each 1 full XYXYX visual output is uniquely identifiable and linked directly to its corresponding `tokenId`

through a visually intuitive and cryptographically robust process.

The Solidity code snippet above defines a set of functions within a smart contract that works together to generate hexadecimal color codes based on a given numeric value and to create unique hashes for token IDs which are then used to determine colors.

### How does it work

Find below a breakdown of XYHASH components and functionality:

**getColorComponentRed, getColorComponentGreen, getColorComponentBlue**: These three functions extract the red, green, and blue components of a color from a`uint256`

value. This is achieved by bit-shifting the value to the right (`>>`

) and applying a bitwise, and operation (`&`

) with`0xf`

(hexadecimal for 15) to isolate the last four bits. The bit-shifting distances (8 for red, 4 for green, and 0 for blue) position the bits of interest in the rightmost position to apply the mask (`0xf`

). The result is cast to`uint16`

and represents the color component value in the range of 0 to 15.**Red Component**: Extracted by shifting the value 8 bits to the right and isolating the last four bits.**Green Component**: Extracted by shifting the value 4 bits to the right and isolating the last four bits.**Blue Component**: Extracted by directly isolating the last four bits of the value.

**_HEX_SYMBOLS**: A private constant byte array containing the hexadecimal symbols '0' to 'f'. This is used to map the numeric color component values (0-15) to their hexadecimal character representations.**getColorHexCode**: This function uses the three color component functions to obtain the red, green, and blue values of a color, maps these values to their hexadecimal characters using the`_HEX_SYMBOLS`

array, and constructs a hexadecimal color code string. The color code string starts with a "#" followed by two characters for each color component, doubling each character for simplicity (e.g., if the red component is`0xf`

, it will be represented as "ff" in the string).**xyHash**: A function that generates a hash value based on a given string prefix and a`uint256`

`tokenId`

. It uses the`keccak256`

hash function on the concatenated string and`tokenId`

, then takes the result modulo 4096*(refers to the mathematical operation known as the "modulo" operation, which finds the remainder when one number is divided by another. In this context, after computing the hash function (likely producing a large integer as a result), the modulo operation is applied with 4096 as the divisor.).*This ensures a fixed range of possible outcomes, which is useful for generating predictable yet unique values for color determination.**getColor1 and getColor2**: These public functions generate color values by calling`xyHash`

with different string prefixes ("1" and "2", respectively), and the given`tokenId`

. The resultant hash values can then be used to determine unique colors for each, potentially for use in generating or coloring tokens.

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