How the PC boots even after the CMOS battery failure?

Whenever I do switch on, my pc boots straightaway. It doesnt wait for me to press the Power button. When I plug the cable and power on, computer also automatically gets powered. So I replaced the CMOS battery and the problem was solved. I have measured the cmos battery with a multimeter and it has only 0.28V(instead of 3V). Now I want to know, how the BIOS gets powered on eventhough the voltage from the CMOS battery is not sufficient. And why my pc is powered on automatically when I do switch on the AC outlet.

Now I want to know, how the BIOS gets powered on eventhough the voltage from the CMOS battery is not sufficient.

The voltage from the "CMOS battery" is only there to keep a tiny amount of CMOS memory, a type that uses extremely little power, from losing its contents, and to run the real-time clock (RTC). THe memory contains your "BIOS" settings. (Should be called firmware settings, since "BIOS" refers to the old PC BIOS standard, where as most all new machines use UEFI firmware instead.) The battery power is not required to "power on" the BIOS when you power up the machine.

In modern motherboards the BIOS settings are stored in NVRAM instead of CMOS memory and require NO power to maintain.

In both cases if you lose the CMOS battery power you will likely lose the clock setting, so the next time it comes up it will be set to some default time. In the former case your "BIOS settings" will be lost, but the default settings are often close enough.

When plugged into a live outlet, and if not switched off via a "hard" power switch, your power supply is always emitting "plus five standby" voltage. (This is marked +5SB in the wiring diagram. The "plus five" refers to its supplying positive five volts with respect to ground.) This output provides an amp or so in most desktop PSUs. It can maintain the CMOS memory and the RTC, so during intervals when the machine is "powered off" but is still receiving +5SB, there is no drain on the CMOS battery. +5SB is what runs the power control circuit on the mobo. When you push the power button on the front panel, that is just a logic input to this circuit, which in turn grounds the ~PS_ON line (normally green) from the PSU; this causes the PSU to turn full on. In moments the PSU asserts PWR_OK, which tells the motherboard that the main voltage rails are within spec. This in turn allows the motherboard to reset the CPU, whereupon the CPU begins running code from the firmware ROM. The first such code is the power-on self test code.

+5SB is also used to keep RAM refreshed when you're in standby (sleep) state, and to provide power to the and to provide power to a few devices, typically a keyboard, mouse, or LAN interface, that are able to wake the system. The "CMOS battery" does not and cannot power these things.