First the computer because we know what is going on there. Not all information is bits but that is the initial bias. Three things happen to information in the computer:
It is read in
Imported into the computer from outside
it is written out
Exported from the computer to someplace outside
it is stored
same place but later time
it is moved
same time (nearly) but different place
it is processed
it is combined with other data and ‘processed’ to produce new data.
We concentrate here on the last three.

Storing Data

Before about 1952 computers would store data by physical positioning of visible parts. Here is a mechanical word oriented binary memory few have heard of. Next came several techniques such as:

Moving Data

In the mechanical days it was turning a shaft, or push/pull on a rod. Upon electronics it was a conductor signaling with a volte or current.

Processing Data

In the mechanical era a piece would move if pushed with a spring, and neither of two obstacles blocked it. This gave an OR like function. Of course there were variations on this.

With electronics came logic circuits that were often electronic analogs to the mechanical ones. The NOR function on two bits was a universal basis for all digital calculation, and was indeed convenient to build and an efficient foundation on which to implement all more complex functions.

Categories of Information in the Computer

First there is the hardware logic diagrams which are fixed at the factory. In the beginning this was thousands of bits of information but today it is perhaps 109 bits or somewhat less if you account for repetitious nature of some parts of the machine. Then there is the ROM which may be fixed at the factory and is merely a cheaper way of including function that is infrequently used and must me there upon power up. Some computers have flash memory which can be occasionally changed in the field and is also there upon power up. Next is RAM which is not there on power up and must be initialized by code stored in ROM or flash, usually by reading from a disk. The last layer of the typical system is the disk which keeps its memory without power.

The Brain

I attest that I am an amateur here!! First there is the DNA which bears on the brain. Then there is (or may be) methylation in the DNA of the germ line that is heritable. Then there is the somatic methylation that is presumably germane to morphogenesis of the brain. Then there is the resulting set of neurons and synapses. As the brain develops in the world synapses disappear and the remaining ones probably acquire long term state; some have suggested that a kilobyte would suffice to hold this state. I suspect that much less is relevant.

All the above information changes very slowly. Ephemeral information includes the electric potential of at least the axons. Response by dendrites depends on the potential of the axons to which they attach and extremely ephemeral dendrite state which may be critical in discriminating variations in pulse trains. I would bet that there are chemical variations in a synapse that last for seconds and bear on the behavior of the synapse.

Some have proposed that long term, but mutable dendrite state may include prions which, in each dendrite, congeal in one of their two stable states, providing thus a bit of information per dendrite.