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One way to construct a circuit that produces an output of 1 regardless of the inputs is to use a simple OR gate. Here is the procedure:

1. Obtain an OR gate IC (Integrated Circuit) such as 7432 or 4071.

2. Connect the power supply pin (VCC) of the IC to the positive terminal of the power supply.

3. Connect the ground pin (GND) of the IC to the negative terminal of the power supply.

4. Connect all the four input pins (pins 1,2,3, and 4) of the OR gate IC together.

5. Connect the output pin (pin 5) of the IC to the LED or any other output device.

6. Connect a proper resistor for the LED in series with the output pin.

7. The circuit is ready for testing. Regardless of the input signals applied to the OR gate, the output will be 1 or HIGH, and the LED will be ON.