Here is a diagram showing the difference in structure between Ripple-Carry adders and Instant-Carry adders. In redstone, Pistons are generally used as the transistors. Using this design, all of the carries are calculate in the same instant, instead of in a ripple. Hence the name

This page summarizes the projects mentioned and recommended in the original post on /r/redstone
Circuit digital-circuits Logisim Simulator logic-gates

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    A digital logic designer and circuit simulator.

    You can use digital to make the diagrams if you want https://github.com/hneemann/Digital

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