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Under the SOFTWARE METHOD – POLLING heading.

What is the meaning of this line?

“In this method, all interrupts are serviced by branching to the same service program”.

https://www.geeksforgeeks.org/priority-interrupts-sw-polling-daisy-chaining/

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it means, you have a file, in that file( service program ) the code is :

if (device[0].flag)
    device[0].service();   // branch to device[0].service() to service device0
else if (device[1].flag)
    device[1].service();  // branch to device[1].service() to service device1
.
.
.
.
.
.
else
    //raise error

polling --- doesn't know which device is cause the interrupt, so we check every time this file and service according to it ( by branching from the file )!

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the "same service programs" refers to the ISR(Interrupt service routine) which is executed when interrupt is raised.

since interrupt is raised from single interrupt request line to which many devices are connected. If more than one device raises an interrupt , a priority or first come first serve basis may be decided for servicing the devices.  So polling is a method in which the servicing is done by checking each device for possible interrupt request. Any device which is found requesting service , it's subroutine is executed by branching from the original ISR , in which conditional branching code for the devices will be contained.

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