• PainterGuy
In summary, an inverter is a gate that can be easily converted into a NAND or NOR. The reason that the digital electronics section of textbooks almost always start with the analysis of an inverter is because the inverter circuit is easier to analyze.
PainterGuy
Hi,

Both NAND and NOR are considered to be universal gates. For example, NAND gates can be used in combination to perform the AND, OR, and inverter operations. The same could be said of NOR gate.

Then, why the digital electronics section of electronics textbooks almost always start with the analysis of an inverter. All the fundamental concepts such as noise margins, W/L, power analysis, etc., are explained in the context of an inverter. If NAND and NOR gates are universal, then, IMHO, those should be used.

What's the reason that the treatment of digital electronics start with an inverter? Is the reason being that the inverter circuit is easier to analyze? Could you please help me with it?

PainterGuy said:
All the fundamental concepts such as noise margins, W/L, power analysis, etc., are explained in the context of an inverter
The inputs of NAND and NOR gates have the same charcteristics as the input of an inverter. The logic functions are internal to the circuit.

PainterGuy
Start simple. The simplest gate to teach and model is the inverter.
It is easy to later change an inverter into a NAND or NOR gate.
NAND and NOR may be universal, but they are not ever-present, nor fundamental.

If you work with TTL logic, you will think in NAND. If you work with CMOS logic, you will think in NOR. If you work with I²L, you will think in terms of inverters with one input and multiple outputs, where the logic is determined by the way the outputs are connected together. https://en.wikipedia.org/wiki/Integrated_injection_logic
If you understand the generalised inverter, you can understand your speciality.

pbuk, PainterGuy and Klystron
Which came first? The chicken or the egg? Stop thinking about gates and think about functions. A NAND gate is made of an AND gate with a NOT gate on the output. The basics functions are AND, OR, and NOT. The basic functions are what should be and are taught first.

Tom.G and PainterGuy
Baluncore said:
If you work with CMOS logic, you will think in NOR.

Averagesupernova said:
A NAND gate is made of an AND gate with a NOT gate on the output.
Maybe in logic but not in electronics.

Averagesupernova said:
The basics functions are AND, OR, and NOT.
Maybe in logic but not in electronics.

Averagesupernova said:
The basic functions are what should be and are taught first.
Yes. The basic TTL gate is an inverter (NOT). This is easily converted to a NAND from which all other gates are derived.

vela
PainterGuy said:
Then, why the digital electronics section of electronics textbooks almost always start with the analysis of an inverter. All the fundamental concepts such as noise margins, W/L, power analysis, etc., are explained in the context of an inverter.
Yes, and in the next chapter you will see that by adding one transistor you convert your (TTL) inverter into a NAND gate with the same noise margins etc.

PainterGuy
PainterGuy said:
Ask a difficult question, and I will have to answer it backwards.
Basically, a TTL output sinks current when low. High signals are most economic. The more high inputs, the less the signal power. A rarely used reset input will idle high to save power, so you must pull it momentarily low to reset the device, which is a form of negative logic. The most economic TTL gate then has most inputs high, which makes it a NAND gate. Once you get over the fact that conventional current flows out of a TTL input, it becomes obvious.

CMOS is a positive logic. A reset pin will stay low until it goes momentarily high to activate the function. To get a high output from an inverting gate, all inputs must be low which makes it a NOR gate.

pbuk said:
Yes, and in the next chapter you will see that by adding one transistor you convert your (TTL) inverter into a NAND gate with the same noise margins etc.
Not quite. To make more TTL NAND gate inputs, you only need to add another emitter to the one input transistor. It may come as a surprise that you can have such a thing as a multiple emitter transistor, or that emitters would be the input to the gate.

PainterGuy
Baluncore said:
Not quite. To make more TTL NAND gate inputs, you only need to add another emitter to the one input transistor.
Good point. Which makes it even more relevant to study first the single emitter case i.e. the inverter.

My advice to the OP is that if he spent less time complaining about what the book is trying to teach him and more time learning then he will make more progress.

hutchphd and anorlunda
@pbuk I did say stop thinking about gates and think about functions didn't I? I suppose I should have said the NAND FUNCTION is made from AND with NOT hanging on the output. My point still stands. If you want to argue that AND is a NAND with NOT hanging on the output I won't stoop to that level if nonsense. Gates are about function. The practical application is certainly important but it doesn't come first.

Tom.G
pbuk said:
My advice to the OP is that if he spent less time complaining about what the book is trying to teach him and more time learning then he will make more progress.

I wasn't complaining about it anything. Was just trying to know if there was any particular reason for introducing an inverter at the beginning.

Baluncore said:
CMOS is a positive logic. A reset pin will stay low until it goes momentarily high to activate the function. To get a high output from an inverting gate, all inputs must be low which makes it a NOR gate.

I should have mentioned it in my first post. In most books, TTL logic is only introduced toward the end and I think the reason could be that it's not that widespread anymore.

My question was about CMOS logic. In most books they start digital electronics with CMOS inverter.

PainterGuy said:
In most books they start digital electronics with CMOS inverter.
Which they should. I can't think of anything simpler. One input, one output.

Averagesupernova said:
Which they should. I can't think of anything simpler. One input, one output.
They should start with a single transistor inverter, so that the delay due to miller capacitance can be understood. A CMOS inverter requires a minimum of two transistors, with twice the miller capacitance.
It took over 20 years for the speed of CMOS to match that of TTL. Many textbooks were written before CMOS matured to the point where it was fast enough to be useful.

PainterGuy and berkeman
PainterGuy said:
I wasn't complaining about it anything.
That's how it came across, particularly
PainterGuy said:
If NAND and NOR gates are universal, then, IMHO, those should be used.

Have you found before that something you have said has been interpreted as arrogant?

Averagesupernova
For the area of a rectangle: Would you recommend teaching integrals to second to third graders instead of showing them simple base times height?

Averagesupernova
PainterGuy said:
All the fundamental concepts such as noise margins, W/L, power analysis, etc., are explained in the context of an inverter. If NAND and NOR gates are universal, then, IMHO, those should be used.
Note that these concepts are about the electronic characteristics of the gate, not the logical function of the gate, so the fact that a boolean expression can be logically implemented using just NAND gates or just NOR gates is irrelevant.

PainterGuy said:
What's the reason that the treatment of digital electronics start with an inverter? Is the reason being that the inverter circuit is easier to analyze?
Yes, that's the reason. Start with the simplest and add on complications later. (You can also think of an inverter as a single-input NAND or NOR gate.)

PainterGuy, berkeman and pbuk
Good replies and answers from all. Thank you.

This is a good time to tie off the thread, IMO.

Averagesupernova

## 1. Why is the analysis of inverters important in digital electronics?

The analysis of inverters is important because they are the fundamental building block of digital circuits. Inverters are used to convert a binary signal from one logic level to another, which is essential for performing logical operations in digital circuits. Therefore, understanding the behavior and characteristics of inverters is crucial for designing and troubleshooting digital circuits.

## 2. What are the key parameters that are analyzed in an inverter?

The key parameters that are analyzed in an inverter include its input and output voltage levels, propagation delay, rise and fall times, and power consumption. These parameters determine the performance and functionality of the inverter and can be used to evaluate its efficiency and reliability.

## 3. How does the analysis of inverters help in designing digital circuits?

The analysis of inverters provides valuable insights into the behavior of digital circuits and helps in designing them with better precision and accuracy. By understanding the characteristics of inverters, designers can optimize the circuit's performance, reduce power consumption, and improve its reliability.

## 4. Can the analysis of inverters be used to troubleshoot digital circuits?

Yes, the analysis of inverters can be helpful in troubleshooting digital circuits. By analyzing the input and output voltage levels, propagation delay, and other parameters, designers can identify any issues or faults in the circuit and make necessary adjustments or repairs to fix them.

## 5. Is the analysis of inverters relevant for all types of digital circuits?

Yes, the analysis of inverters is relevant for all types of digital circuits. Inverters are used in various digital systems, such as logic gates, flip-flops, and memory units, and their behavior and characteristics are essential for understanding the overall functionality of these circuits.

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