"I'm sorry you can only have 32 colours on screen at once". Then someone came up with HAM.
From
http://amiga.emugaming.com/ahistory.html:
"In the AUI interview Jay Miner describes his experience of viewing of a military flight simulator developed by Singer-Link. Impressed by what he saw, Miner begins to consider the use of blitters to improve the graphics capabilities. This is eventually developed into HAM (Hold and Modify) during 1985. This made it possible to display 4096 colours at the screen by changing the colour registers. However, early reports suggest that he was willing to remove these capabilities when he realized how slow it was. It was only when the motherboard designer informed him its removal would leave a hole in the middle of the motherboard that he accepts that it will be present in the final version - a wise decision that would distinguish the Commodore Amiga from its Atari rival many years later."
HAM(6) is present on all Amiga hardware, except the very first test hardware.
"I'm sorry you've only got 2mb chip memory". Then someone came up with FBlit.
FBlit cannot really work around the 2MB chip memory limitation. What FBlit does, is to make it possible to use fast memory for *offscreen* bitmaps. This definetely is an improvement, but certainly doesn't have much to do with the 2MB chip memory limit, other than leaving the actual chip memory for the displayed bitmaps.
FBlit's main advantage is that on fast 68k cpu, the CPU is faster for blit operations than the blitter itself, esp. since in best cases both source and destination planes are in fast memory.