This page lets you simulate the behaviour of arbitrary collections of logic gates.
To see some ideas of what is possible, try looking at the Presets menu, where you'll find several pre-built circuits. Click the play button to start the simulation. Wires are shown in red when they are high (i.e. one), and in black when they are low (i.e. zero).
Building your own circuits
Click on the buttons below the canvas to select which component you'd like to add to your design. Then click on the canvas to place it. You can move components around by dragging them with the mouse. To move the nodes of wires, you need to select the Move tool first.
Note that nodes are only connected to one another if they are on top of each other. You cannot connect a component mid-way along a wire.