I submit that the complexities of the tasks and uses that computers are used for in ships do not scale with their size.
I do not believe the complexity of whatever physics are involved to calculate a ship jump change in any dramatic way with the size of the ship. The math used to navigate the Voyager Probe is identical to that of the Space shuttle. The Space shuttle might have a few more thrusters to play with.
Specifically, I don't think it takes "1MB of memory per dTon of ship displacement" to calculate a jump, or whatever measure you want.
I do not believe that the computer size is in any dramatic way tied to the displacement of the ship. For example, I'm confident that the there are more computers on a modern naval destroyer than on a Super Tanker, despite the fact the latter vastly out displaces the former.
I am not swayed by the "space ship computer are super duper uber hardened" argument. If you want to apply that to YTU, that's fine, but be consistent and effectively eliminate all other electronics on your ships, weapons (sorry, that gauss rifle doesn't work in space -- the firing computer crashed, nor does that holo sight), combat armor, vehicles, vacc suits etc. as they are NOT hardened. Or if they are, then they manage to do it in small spaces.
There's a nice "adventure" moment. "Looks like some remote solar flare fried out the air raft again..."
Computers scale to the tasks they perform. If the task is roughly the same, the size will be roughly the same. For example, do you think the Engine Control Unit in your car is vastly different in size or capacity than the one in, say, a motorcycle? or a large Kenworth tractor? All of these will fit in your hand. If the Kenworths is larger, it's because it can be vs say the one on the motorcycle. Perhaps the Kenworth one is cheaper than the motorcycle one because the motorcycle one must be smaller as space is at a premium vs a Kenworth. But the problem they are all solving is effectively identical. Mapping fuel injector solenoids to an air sensor, RPM, etc. I'd argue that the ECU for that 14 cylinder, 100K HP diesel container ship motor (1.5M in^3 displacement) is not dramatically larger than the ECU for a diesel truck. More wire, perhaps some more sensors, more displays, but the computer driving it all is 1 to 2 square inches big with a couple RAM chips. Amazing.
What does scale with displacement? Well, wires, cables, conduit, etc. for one. These certainly consume space. I have conduit in my house, but it's contained within the walls, so conduit costs ME (effectively) zero space. Ships might have solid bulkheads, thus requiring such cables to consume extra space. Or, perhaps they can be routed along with the assortment of air ducts and other life support infrastructure.
What else might scale? Well, obviously the demands of a single turret may well be different than 100, or 1000 turrets (though I'd argue not by much). I'd also argue that the control functions would be locally driven by the mount (fire control computer tell turret computer (the one the size of a stick of gum) "point turret to 14 degrees", turret replies "turning", "done", or "stuck"). Mind, number of turrets are only indirectly related to displacement. While a scout ship can't mount 1000 turrets, and large ship could only mount a single turret.
Lets take as an example a ship that operates as a tug. Alone, the ship isn't very big. Some oversized thrusters and maybe extra fuel. But as soon as it hooks up to a large payload (a large, dumb payload mind), all of a sudden "the ship" suddenly grows to 10 times it's normal displacement. Should it suddenly need a larger computer? Has it's problem domain really dramatically changed? That block it's latched on to is dead weight. Maybe, like a tow truck, someone will drag some tail lights to the other end of the payload. But did this ship become ten times more complicated? Hardly. Merely fatter and heavier.
A harbor tug does not adopt the complexity of an aircraft carrier simply because it's pushing it out or towing it in. Harbor tugs are bone stupid. Aircraft carriers are not.
Finally:
http://www.sun.com/products/sunmd/s20/index.jsp
A CRAP load of MIPs and storage in 2dTons. Today. Right now. Off the shelf.
Everything in the ship is a computer: the gun mounts, the weapons, the sensors, the doors, the toilets, the refridgerators, the power plants, door bells and landing lights. The space consumed by "the computer" is interconnecting them all, and workstations/displays to manage it, making the ship a single combined whole. I could run the back office of a 200 person company for 5 years off of an iPhone (not just the CPU, RAM and storage as well). All of the space will be taken up by the printers and terminals. The CPU is invisible.
Controls are all that matter. Those are the things that need to be counted.