## Uniswap V3 Tick Bitmap and Position In Uniswap V3, liquidity positions are defined by a lower and upper tick. These two ticks are stored in a mapping called the tick bitmap. During a swap, the next tick where liquidity exists is located by calling a function called `nextInitializedTickWithinOneWord`. We'll explore how this function works to find the next tick. The tick bitmap is a mapping from `int16` to `uint256`. A tick, which is an `int24`, is broken into two parts. The first 16 bits of the tick, moving from left to right, are stored as an `int16`. This is called the word position. The next 8 bits are stored as a `uint8`, which is called the bit position. For example, let's say we have a tick equal to `-200697`. The first 16 bits converted into a decimal are equal to `-784`. The last 8 bits are converted into the decimal `7`. The process of storing the tick in the tick bitmap looks like this: 1. Break the `int24` tick into an `int16` word position and a `uint8` bit position. 2. Using the word position, access the `uint256` value in the tick bitmap mapping. 3. Create a mask consisting of 256 bits set to zero, except for a single bit set to one at the index of the bit position. ```javascript mask = 0000...0010000 ``` 4. Perform an exclusive or with the current value of the tick bitmap at the word position. ```javascript current_value XOR mask ``` 5. This will set the bit at the bit position to `1` if it was `0` or vice versa, leaving the other bits unchanged. The process of getting a tick from a tick bitmap looks like this: 1. Get the first 16 bits which represent the key for the tick bitmap. ```javascript first 16 bits = 1111111100111100 ``` 2. The tick bitmap will return a `uint256`. ```javascript uint256 = 0111....010 ``` 3. Think of the `uint256` as a sequence of 256 bits. 4. Let's say that we want to convert a bit at the 7th index to a tick, then we rewrite 7 as 8 bits. ```javascript 7 = 00000111 ``` 5. Append these 8 bits to the 16 bits we got earlier to retrieve the tick. ```javascript tick = 1111111100111100 00000111 ```