Where do bytes come from if each gate outputs only all 1s or all 0s?

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Each signal that arrives at a gate cannot be a byte, or if it is, can only be 11111111 or 00000000. Also the outcome of each gate is 000...000 or 111...111. So where are the bytes?

(The question might be wrong but if I knew the right question I guess I would had known the answer too).
 
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Gates usually only handle one bit at a time, as you suggest.

There may not actually be any bytes.

One good example is a frequency counter.
You have a stream of pulses coming into one input of a gate.
Another input has a very precise pulse applied to it. This pulse might last for exactly one second.
So exactly one second's worth of pulses is allowed through to a counter.
So, you get a reading of how many pulses there are per second. That is the frequency of the incoming signal, which is the function of the instrument.

Gates are used in many different ways and quite a lot of them don't involve forming bytes.
When they are, they can be used in sets of 8 or 16 to produce a parallel output of one byte.
Or, there can be a clock which produces the byte as a sequence of 1s and 0s one after the other.