Circuit sandbox

Since $NOT$ , $AND$ and $OR$ are truth-functionally complete, every Boolean function has a circuit — and usually many, which is where the engineering starts. A function can be built from relays or from gates, with more components or fewer, and the sandbox is where you find out which of your attempts actually computes what you wanted.

Scope. Two inputs, one output, and at most twenty components, all combinational: no clock, no memory and no feedback.

Add components, wire an output dot to an input dot, and flip the switches. The table beside the canvas reports the function your circuit computes, for all four combinations of $X$ and $Y$ , and updates as you wire.

Connection controls

Using it

Every component is available from the start: the seven gates, and both relays with the fixed power supply below them. Drag a component to move it, or nudge a selected one with the arrow keys; Escape cancels a wire you started by mistake. An input can take several sources at once, which puts them in parallel — the relay reading of $OR$ . Unconnected inputs leave the output unknown, shown as ? in the table, and feedback loops are rejected: these circuits are combinational, with no memory of earlier inputs.

Nothing is saved when you leave the page, so copy anything you want to keep.

In the book

Chapter 4 · Implementing Booleans builds the three operators out of relays.
Chapter 4 · Adders chains them into binary addition.
Chapter 5 · Checking a circuit turns a finished circuit back into a satisfiability question.