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docs(mdbook): minor change in the bitwise chiplet #1109

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Oct 19, 2023
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docs(mdbook): minor change in the bitwise chiplet #1109

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4 changes: 2 additions & 2 deletions docs/src/design/chiplets/bitwise.md
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Expand Up @@ -22,7 +22,7 @@ To perform this operation we will use a table with 12 columns, and computing a s

In the above, the columns have the following meanings:

- Periodic columns $k_0$ and $k_1$. These columns contain values needed to switch various constraint on or off. $k_0$ contains a repeating sequence of a single one, followed by seven zeros. $k_1$ contains a repeating sequence of seven ones, followed by a single zero.
- Periodic columns $k_0$ and $k_1$. These columns contain values needed to switch various constraints on or off. $k_0$ contains a single one, followed by a repeating sequence of seven zeros. $k_1$ contains a repeating sequence of seven ones, followed by a single zero.
- Input columns $a$ and $b$. On the first row of each 8-row cycle, the prover will set values in these columns to the upper 4 bits of the values to which a bitwise operation is to be applied. For all subsequent rows, we will append the next-most-significant 4-bit limb to each value. Thus, by the final row columns $a$ and $b$ will contain the full input values for the bitwise operation.
- Columns $a_0$, $a_1$, $a_2$, $a_3$, $b_0$, $b_1$, $b_2$, $b_3$ will contain lower 4 bits of their corresponding values.
- Output column $z_p$. This column represents the value of column $z$ for the prior row. For the first row, it is set to $0$.
Expand All @@ -32,7 +32,7 @@ In the above, the columns have the following meanings:

Let's illustrate the above table on a concrete example. For simplicity, we'll use 16-bit values, and thus, we'll only need 4 rows to complete the operation (rather than 8 for 32-bit values). Let's say $a = 41851$ (`b1010_0011_0111_1011`) and $b = 40426$ (`b1001_1101_1110_1010`), then $and(a, b) = 33130$ (`b1000_0001_0110_1010`). The table for this computation looks like so:

| a | b | x0 | x1 | x2 | x3 | y0 | y1 | y2 | y3 | zp | z |
| a | b | a0 | a1 | a2 | a3 | b0 | b1 | b2 | b3 | zp | z |
| :---: | :---: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :----: | :---: |
| 10 | 9 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 8 |
| 163 | 157 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 8 | 129 |
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