Add documentation
diff --git a/LICENSE b/LICENSE index 261eeb9..a45ecfb 100644 --- a/LICENSE +++ b/LICENSE
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diff --git a/README.md b/README.md index d2efa54..fe94257 100644 --- a/README.md +++ b/README.md
@@ -1,10 +1,38 @@ -# Caravel User Project +# Universal gates -[](https://opensource.org/licenses/Apache-2.0) [](https://github.com/efabless/caravel_project_example/actions/workflows/user_project_ci.yml) [](https://github.com/efabless/caravel_project_example/actions/workflows/caravel_build.yml) +It is quite well known that any logic circuit can be built using only NAND gates. +For instance, an XNOR gate is equivalent to the following construction: -| :exclamation: Important Note | -|-----------------------------------------| +>  -## Please fill in your project documentation in this README.md file +Such gates are called universal. Any Boolean function with 2 inputs and 1 output can be built from at most 5 NAND gates. -Refer to [README](docs/source/index.rst) for this sample project documentation. +We can also define a gate <i>U</i><sub>21</sub> that is universal in a stricter sense, such that any Boolean +function with 2 inputs and 1 output is realized with just a single copy of <i>U</i><sub>21</sub>. +This gate would obviously need more than 2 inputs, but it's usually still more economical than the <i>2k</i> inputs +and <i>k</i> outputs used from a set of NAND chips (1≤<i>k</i>≤5). + +>  + +As an example, this is how we get the NAND of <i>p</i> and <i>q</i> and the XNOR of <i>p</i> and <i>q</i> +by wiring up <i>U</i><sub>21</sub>'s four inputs <i>a</i>, <i>b</i>, <i>c</i> and <i>d</i> +to a suitable combination of <i>p</i>, <i>q</i>, 0 and 1: + +>   +> +> ⮟ ⮟ ⮟ ⮟ ⮟ ⮟ ⮟ ⮟ ⮟ ⮟ ⮟ +> +>   + +So <i>U</i><sub>21</sub> stands in for any combinatorial logic with 2 inputs and 1 output. +And any Boolean function with 3 inputs and 1 output can be built with at most 3 copies of <i>U</i><sub>21</sub>. +But that doesn't stop us from creating a gate <i>U</i><sub>31</sub> that's <i>even</i> more universal +and does so with a single copy when wired correctly: + +>  + +This repository contains a chip design with four independent gates +<i>U</i><sub>21</sub>, <i>U</i><sub>31</sub>, <i>U</i><sub>41</sub> and <i>U</i><sub>22</sub> +where each <i>U<sub>ij</sub></i> can be wired to act as an arbitrary function +with <i>i</i> inputs and <i>j</i> outputs. +It uses the caravel framework and is hardened for the gf180mcuC technology platform.
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