Question about 1-bit Analog-to-Digital Converter
You have grossly changed the question, so I'm writing a whole new answer.  However, while the new version does clear up some things, it still leaves a lot of questions unanswered (despite having been specifically asked by several people), and continues to exhibit misconceptions.  The easiest way to go thru this is to respond to individual pieces of your question:

Device 1 outputs an analog signal.

No, it clearly doesn't.

This analog signal will stay at voltage low until it pulses for some time t to high. Then it will return to voltage low. This analog signal will always be either at voltage low or high.

Then it's not a analog signal.  It clearly has only two possible states.  You said before that T is fixed.  This is a sequence of pulses.

The important question, which you have been asked repeatedly, is what is the meaning of this signal.  The voltage levels are fixed, the pulse high time is fixed, so information can only be encoded in the pulse low time.  You said previously the timing of these pulses are "random" (your word).  If that is true, this pulse sequence carries no information at all, in which case this whole execise is pointless.  I expect you meant that the pulse times are unpredictable, which is very different from random.  That still leaves the question of what data is this pulse sequence carrying, and how exactly is it encoded?

Device 2 wants to read this signal. However, it can only receive signals with a UART protocol at its internal baud rate.

OK, so what is this baud rate?  Note that this will inherently limit the bandwidth of the information that device 2 can receive.  The fastest common UART speed is 115.2 kBaud, but it can be faster.  However, anything over 1 Mbit/s is very unlikely.

Interpreter is what I want.

No, this interpreter is what you imagine as a solution.  What you want is apparently to transmit the information encoded in the pulse stream over a UART to device 2.  I'll skip the rest of your question since it's pointless detail about your imagined solution instead of the actual problem.

Now that the actual problem is somewhat more clear, what we need to know is also more clear.  To come up with something that goes between the pulse stream and the UART, we need to know:

What kind of data is being encoded in this pulse stream?  Is it a single scalar value?  It would help to know what it physically represents.

What is the fixed pulse high time?

What is the minimum possible pulse low time?  This together with #2 also tells us the maximum pulse frequency.

How exactly is the data value encoded in this pulse stream?

What is the UART baud rate that device 2 expects?

What are the high and low voltage levels of the pulse signal?



I expect clear and specific answers to each of these questions, else I'm outta here.  These are all asked for a reason.  They all need to be answered whether you understand why they are asked or not.  And no, you don't get to "interpret" these questions and ask what you think I want to know or what you'd rather tell me.

Added

You have now given real specs on the incoming pulse stream.  It is coming from a photon detector, and each pulse represents a photon.  The signal is TTL digital, with low &le; 800 mV, and high &ge; 3.5 V.  Each pulse lasts 30 ns, and there is at least 50 ns between consecutive pulses.  This means the minimum pulse period is 80 ns, and the maximum pulse frequency 12.5 MHz.

The task is to somehow communicate the information in this pulse stream to a second device over a UART connection.  The UART baud rate is not known, so for now I'll assume the fastest common rate of 115.2 kBaud.

Electrically receiving the pulse signal is easy since anything with a TTL compatible input will work directly.  This could be, for example, any 74HCTxxx gate running at 5 V.  Ordinary CMOS inputs may not work, depending on what their minimum guaranteed logic high level is.  The datasheet of whatever is receiving this signal needs to be checked, but finding something compatible will not be a problem.  Other than chosing the right digital input to receive this signal, nothing special needs to be done.

To design the thing between the pulse stream and the UART, we need to know what information from the pulse stream is relevant.  Do you only care about the average light level?  If so, what is the highest frequency of the light level you care about?  Or, do you need to know when individual pulses occur?  That would be much harder.  The basic problem is that there is much more information in the pulse stream than you can possibly communicate over the UART connection.  Therefore, some data reduction must be performed.

Let's take a first pass look at the magnitude of the data reduction.  Suppose you only needed to know photon counts per time interval.  Each UART byte takes 10 bit times at 115.2 kBaud, so 87 &micro;s.  At the maximum pulse rate of 12.5 MHz, there can be up to 1085 pulses per UART byte.  Since a byte can express 0-255, you could scale the number of pulses observed every byte time by .235.  That would give you the light level resolved to roughly 4 photons sampled at 11.5 kHz.  The maximum light level frequency is therefore 5.7 kHz.  Is that good enough?

A possible trick is to transfer the error from the previous byte to the next byte.  That gives you the long term count down to single photons at the expense of some noise on each reading.

Another possibility is to send two bytes each count interval.  Now you can have up to 2170 counts per sample interval, but that can be directly transmitted in two bytes.  You get full resolution, but the maximum frequency goes down to 2.9 kHz.  With a little cleverness you can pack two readings into 3 bytes to get full resolution at a higher frequency, although with more latency.

There are a lot of possible data reduction schemes.  It is impossible to pick one without knowing what aspect of the data you care about.