user11779: My understanding has been that the Serial transmission is indeed done (on the Arduino Uno) via the pins named TX->1 and RX<-0?
With this I assume that the Atmega has a machine code that would allow in 1 or processor cycles (125 or 62.5 ns) to set a byte (i.e. Port byte DDRD) as to forward exactly one bit of information for further processing to the ATmega16U2 "serial to USB" chip?
If this is true I would expect that 1 Byte = being 8 bits would require a discouragingly slow 8 to 12 cpu cycles (500ns to 1us)? Is this true?

user10794: According to the datasheet:

Running at 16 MHz (as the Uno does) you can get up to 2 Mbps.

If this is true I would expect that 1 Byte = being 8 bits would require a discouragingly slow 8 to 12 cpu cycles (500ns to 1us)? Is this true?

For a bit or a  byte? At 2 Mbps that is a bit every 8 clock cycles. 

would you know what would the UART be?

The UART is built into the processor chip. I suggest you read the datasheet.

I thought it was unable to tell more than 16 million times a second something to the UART, which then could have baud rates higher than what could be indicated by the Atmega328 on the Uno, right?

You can't do anything more than 16 million times a second at 16 MHz. And the clocking out of bits (in SPI, serial, or I2C) itself requires clock cycles, although they are done in parallel with the processor instructions by the hardware.

This is related to your other thread Can Arduino Uno's serial handle to foward push through 1-wire protocol? isn't it? Your end objective, I am guessing, is to try to implement 1-wire reading/writing via sending each bit via serial. This is just not the right way to achieve that objective.
In fact this thread in particular is coming across as an X-Y problem - your stated objective of wanting high-speed serial, is not really the problem you are trying to solve, is it?

user4143: No, it is not true.
You are assuming (wrongly) that the CPU is doing the UART communication.  It isn't.
The UART is a completely separate piece of hardware inside the chip.  It runs by itself.  The CPU merely places the byte to transfer into a special function register (SFR).  The UART then takes that and clocks it out through the IO pins at the right rate for the serial communication.  While that is going on the CPU is free to perform other operations.
The CPU can then either consult another SFR to determine if the transmission has finished, or utilize an interrupt that the UART will trigger when the transfer has been completed.

11779: <p>My understanding has been that the Serial transmission is indeed done (on the Arduino Uno) via the pins named <code>TX-&gt;1</code> and <code>RX&lt;-0</code>?
With this I assume that the Atmega has a machine code that would allow in 1 or processor cycles (125 or 62.5 ns) to set a byte (i.e. Port byte <code>DDRD</code>) as to forward exactly one bit of information for further processing to the <code>ATmega16U2</code> "serial to USB" chip?</p>

<p>If this is true I would expect that 1 Byte = being 8 bits would require a discouragingly slow 8 to 12 cpu cycles (500ns to 1us)? Is this true?</p>
 10794: <p>According to the datasheet:</p>

<p><a href="https://i.stack.imgur.com/pXJhh.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/pXJhh.png" alt="Baud rates at 16 MHz"></a></p>

<p>Running at 16 MHz (as the Uno does) you can get up to 2 Mbps.</p>

<blockquote>
  <p>If this is true I would expect that 1 Byte = being 8 bits would require a discouragingly slow 8 to 12 cpu cycles (500ns to 1us)? Is this true?</p>
</blockquote>

<p>For a bit or a  byte? At 2 Mbps that is a bit every 8 clock cycles. </p>

<blockquote>
  <p>would you know what would the UART be?</p>
</blockquote>

<p>The UART is built into the processor chip. I suggest you read the datasheet.</p>

<blockquote>
  <p>I thought it was unable to tell more than 16 million times a second something to the UART, which then could have baud rates higher than what could be indicated by the Atmega328 on the Uno, right?</p>
</blockquote>

<p>You can't do <em>anything</em> more than 16 million times a second at 16 MHz. And the clocking out of bits (in SPI, serial, or I2C) itself requires clock cycles, although they are done in parallel with the processor instructions by the hardware.</p>

<hr>

<p>This is related to your other thread <a href="https://arduino.stackexchange.com/questions/16032/can-arduino-unos-serial-handle-to-foward-push-through-1-wire-protocol">Can Arduino Uno&#39;s serial handle to foward push through 1-wire protocol?</a> isn't it? Your end objective, I am guessing, is to try to implement 1-wire reading/writing via sending each bit via serial. This is just not the right way to achieve that objective.</p>

<p>In fact this thread in particular is coming across as an <a href="http://xyproblem.info/" rel="nofollow noreferrer">X-Y problem</a> - your stated objective of wanting high-speed serial, is not really the problem you are trying to solve, is it?</p>
 4143: <p>No, it is not true.</p>

<p>You are assuming (wrongly) that the CPU is doing the UART communication.  It isn't.</p>

<p>The UART is a completely separate piece of hardware inside the chip.  It runs by itself.  The CPU merely places the byte to transfer into a <em>special function register</em> (<em>SFR</em>).  The UART then takes that and clocks it out through the IO pins at the right rate for the serial communication.  While that is going on the CPU is free to perform other operations.</p>

<p>The CPU can then either consult another <em>SFR</em> to determine if the transmission has finished, or utilize an interrupt that the UART will trigger when the transfer has been completed.</p>
