A kit for this project is available from RSH Electronics.
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This project flashes eight LEDs in an apparently random manner. It uses a 4026 combined counter and display driver IC which is designed for driving 7-segment LED displays. The sequence is not really random because seven of the LEDs would normally be the display segments, the eighth LED is driven by an output that is normally used for driving further counters. The table below shows the sequence for the LEDs. You can use less than eight LEDs if you wish and the table may help you decide which ones to use for your purpose.
This project uses a 555 astable circuit to provide the clock pulses for the 4026 counter. Resistors are not required for the LEDs because the 4026 IC limits the current to about 5mA for each LED.