Systems designers are free to use whatever interrupt architecture they wish but IBM PCs use the Intel 82C59A-2 CMOS Programmable Interrupt Controller [6, Intel Peripheral Components,] or its derivatives. This controller has been around since the dawn of the PC and it is programmable with its registers being at well known locations in the ISA address space. Even very modern support logic chip sets keep equivalent registers in the same place in ISA memory. Non-Intel based systems such as Alpha AXP based PCs are free from these architectural constraints and often use different interrupt controllers.
Figure 
shows that there are two 8 bit controllers chained together; each having a mask and
an interrupt status register, PIC1 and PIC2.
The mask registers are at addresses 0x21 and 0xA1 and the status registers
are at 0x20 and 0xA0
Writing one to a particular bit of the mask register enables an interrupt, writing
a zero disables it.
So, writing one to bit 3 would enable interrupt 3, writing zero would disable
it.
Unfortunately (and irritatingly), the interrupt mask registers are write only, you cannot read back the value
that you wrote.
This means that Linux must keep a local copy of what it has set the mask registers to.
It modifies these saved masks in the interrupt enable and disable routines and writes
the full masks to the registers every time.
When an interrupt is signalled, the interrupt handling code reads the two interrupt status registers (ISRs). It treats the ISR at 0x20 as the bottom eight bits of a sixteen bit interrupt register and the ISR at 0xA0 as the top eight bits. So, an interrupt on bit 1 of the ISR at 0xA0 would be treated as system interrupt 9. Bit 2 of PIC1 is not available as this is used to chain interrupts from PIC2, any interrupt on PIC2 results in bit 2 of PIC1 being set.