Electronic – Help between 2n2222 and 2n2222a

You should really use (timer) interrupt driven firmware to ensure your clock ticks accurately. Software delays will cause a gradual drift because of variations in your program flow. Here is a good overview of how to use Timers on the Arduino platform. You can follow something like the pattern described in the section on "Blinking LED with timer overflow interrupt". The Arduino's 16MHz crystal is plenty accurate for a toy clock project if you write the software correctly.

This style of writing software is "event-driven," so you have to get your mind around that first. The hardware tells you something happened (in this case a second has passed) and your software reacts to it. Instead of you telling your software to "wait a second" and then doing something.

The output high voltage from the emitter of Q1 will never exceed Vb-Vbe. If the maximum base drive voltage is 5V, then the emitter will never be able to rise above approximately 4.3 volts when Q1 is saturated.

If the power supply increases to 5.9 Volts, then the transistor is operating in a linear region and the difference of 5.9-4.3 is dissipated across the CE junction. As soon as the emitter tries to rise up, it clamps off the base and shuts down a little until it reaches equilibrium. If the trace you show is of the actual circuit and not of a simulation, then the ringing is most likely cause by some noise source in the circuit as 1Hz is to slow for it to be a transient response.

The upper end of R1 never floats. It is bound by the Vbe junction of Q1.

If you wish to use a high side driver, then perhaps consider a PNP device. If you want a low side driver, then use an NPN device. this will free R1 from Vbe.