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Theory Of Operation
A ROM is an array of storage locations indexed by a binary-encoded address at the address pins of the chip. The standard 512kB Amiga ROM is 256k x 16-bit words, addressed by pins A0-A17. Larger ROMs require an extra address pin for each doubling of capacity: A18 (1MB), A19 (2MB), and so on.
These larger ROMs can be considered a banked (or multi-ROM-image) version of the 512kB ROM: A0-A17 address the currently selected 512kB bank (aka ROM image), while A18+ select between 2 or more banks.
The purpose of the Kickstart switcher, then, is to control the bank-selection pin(s). Since this design can switch between up to 8 ROM images, it controls up to 3 address pins (A18-A20) via outputs PB12-PB14. A0-A17 remain under control of the Amiga hardware.
The switcher defaults to image 0 at startup. The next image is selected when it sees a low pulse at pin PA8 which is longer than 3 seconds. The input is expected to be attached to the active-low reset line of the Amiga, so that holding Ctrl-Amiga-Amiga for multiple seconds will trigger the Kickstart switch.