I am confused as to how this circuit is complete and hence how electricity flows through it.
Petzold explains earlier in the book that the V refers to a battery connected to ground the way in which I have drawn it. If electrons are taken from the earth at the light bulb and flow towards the leftmost NOR gate, where do the electrons go from here? How is the circuit complete?
I understand that this may be a silly question but I’d appreciate the help.
See, gates have a Vcc. They don't turn LOW into HIGH voltage out of nowhere.
Gates are made up of transistors. Let me explain this to you with a simple NAND gate.
simulate this circuit – Schematic created using CircuitLab
When at least one of the inputs is low, the Vcc supplies current to the LED since the MOSFETs don't allow current to pass. This causes the LED to glow at (0,0) (0,1) and (1,0) inputs.
When both inputs are high, current passes through the MOSFETs into the ground with little to no current going into the LED since the former is the lowest resistance path. This causes the LED to not glow at (1,1) input.
So you see, the reason the LED glows is because of the Vcc. The LOW input is not magically turned into a high input. The gate inputs simply allow/deny current to pass through different parts of the circuit.
Each of the gates also has connections to the supply voltage and ground, which are not shown. It is often implied in circuit diagrams that active components (chips) without an explicit supply connection are connected to a common power supply.
The gates simply take the power needed to drive their outputs (and therefore the lamp) from the common power supply, which has been omitted in the diagram.
In particular, the electrons flow through the lamp and reach the positive supply voltage through the rightmost NOR gate directly.
The gates actually look like this:
simulate this circuit – Schematic created using CircuitLab
(I couldn't quite draw the supply connections of the gate correctly, but I hope it gets the point across.)
The (technical) current flows from the supply voltage into the NOR gate's power supply connection, then out from the NOR gate through the lamp and finally back to the other side of the supply.
The diagram below replicates your second circuit. SW1 has just opened. The red wires indicate the same as in your circuit. They indicate where the digital circuit is a logical 1. (5V in this case).
I have added the power connections to the NOR gates that are usually omitted for logical clarity. I have also added all the "ground connections" that are "understood" to be there. These are necessary to properly demonstrate the closure of the electron's path.
Where do the electrons go from here? How is the circuit complete?
The blue arrows indicate the path and direction the electrons that flow through the lamp take. The electrons flow into the NOR2's output and then up to the 5V rail, through the 5V source, then back to the lamp, completing their closed path.
The green arrows show the direction of the electron flow through the NOR1 gate's input. The electrons flow up from ground into NOR1, then out of the input, then all the way to NOR2's output where they join with the lamp's electrons. They flow together until they reach NOR1's ground terminal where the "green electrons" split off completing their closed path.
simulate this circuit – Schematic created using CircuitLab
The flow through NOR1's input is very small (almost zero for CMOS). The open switches do not guaranty a low voltage. Some circuitry has been omitted by the author of the book. Other electron flows can be added to the drawing, but what I have shown should be sufficient to clarify how the electrons flow.
Hope this helps.
For a book that professes to be "The Hidden Language of Computer Hardware and Software" they sure seem to miss the mark here. (book ref here)
tl, dr version: there is no current flow. The text shown is a behavioral logic model, using switches and lamps as metaphors for logic inputs and outputs of ‘1’ and ‘0’ or ‘high’ and ‘low’. They aren’t representing actual physical devices. In this diagram they only represent logical values and behaviors.
I came to to this conclusion after having a peek at some of the interactive sims the author uses. They rely heavily on these switch-and-lamp metaphors, until they don’t.
Earlier in the book they show relay logic, and as such hints at physical behaviors: switch closes, coil energizes, contacts close, current flows to the lamp.
They then transition to logic gates, which are behavioral symbols representing Boolean equations (but nonetheless can also have physical representations, as we’ll see below.)
Even later in the book, the author dispenses with the switches-and-lamps metaphors, going full behavioral logic using 1’s and 0’s.
Back to this troublesome diagram. Being behavioral symbols, the ‘switches’ and ‘lamp’ don’t draw or supply current any more than a math equation does. They’re representing logic values, using a connection to ‘V’ as a logic ‘1’ and non-connection as ‘0’.
For this diagram then, we’re in Boolean town. Replace those metaphors in your mind with logic ‘1’ / logic ‘0’ and forget about current or electrons.
Fortunately we’re not constrained by the author’s metaphors. We can move between the logical and physical using an online, interactive tool: Falstad.
With Falstad (and other sims, including CircutLab here on this website) we can make a working NOR latch as a symbolic logical model with gates, and as physical one with real devices showing how current flows (simulate it here):
What’s going on?
The left-hand sim shows the NOR latch logic gate diagram - the behavioral model. The power connections are not shown, but implied to be 5V. (In the sim, you can edit each gate to change this voltage.) Set the latch by manipulating the upper switch, see that current flows from the ‘hidden’ power connection in the NOR symbol to the bulb, just like in the textbook diagram. (A lot of current flows into that bulb - its resistance is quite low until the bulb warms up: Falstad is modeling a lamp’s physical behavior.)
The right hand sim shows two CMOS NOR gates each constructed from FET switches - the physical model. Here, the power and ground connections are explicit. Manipulate the upper switch to set the latch, and observe the current flows from 5V, through the lower gate's p-FET, then to the lamp. (The series resistor is a hack to make the sim converge because of the bulb’s low starting resistance.) It, too, operates the same as the text.
Logical or physical, they both work. Most of the time, logical is more convenient to think about and more efficient to simulate. For these reasons, the bulk of digital design work is done in the behavioral logic realm.
But in the real world, physical behavior matters too. Many of the questions here on EE Stackexchange are in fact about how physical digital hardware actually works. Stuff like voltage levels, current paths, switching speed, and so forth.
You will see both languages spoken here: the purity of Boolean logic, and the complexity and analog-ness of devices that implement it. As designers and users of logic devices it pays to be fluent in both.
Now that you have a bit of insider knowledge, I have another issue with this text. They show simple single-pole switches connecting gates to a voltage, which we now understand to be a metaphor for a digital 1 or 0. Beware: this isn't realistic. Gate inputs need to be driven explicitly high or low, especially CMOS, for gates to work properly.
In fact, if you tried to breadboard the textbook circuit as-is using SPST switches with CMOS or TTL gates, it will fail. That's why my sim uses SPDT (single-pole, double-throw) switches that connect to 5V or GND to the inputs.
Why? Here's how different logic families behave with an unconnected input:
Falstad has simulations of these different gate technology types (CMOS, RTL, DTL, TTL) that you can try. This will help you get a sense of how real-world gates behave.
Another detail: Falstad's logical gate sim defaults unconnected inputs to '0'. So in the left-hand sim, the switches could be SPST, just like the text. I didn’t do that because I’m trying to show good practice.
Speaking of good practice, if you were to code this NOR latch in a hardware description language like Verilog or VHDL, the compiler would give you a warning about an unconnected input, and your sim would show the output as unknown, or ‘X’.
Just remember, don't get caught out by that rookie mistake. Connect gate inputs to a valid logic level, even the unused ones. Even in Verilog.
Oh, and there’s another problem in physical-land too: incandescent lamps need a lot of current until they’re warmed up. That’s why I had to add a series resistor to the physical sim. Were you to use a lamp in a breadboard lash-up, it would likely fail because the lamp would not allow that lower gate to be driven high to set the latch. This would be especially true for TTL which has weak high-drive; RTL and DTL wouldn’t work at all.
This problem could be fixed by adding a buffer to drive the lamp, or by using an LED with a series resistor.
Identifying and solving problems like these is where fluency in both logical and physical really helps.
The takeaway: the book is introductory, confuses logical and physical, and if taken literally could get you into trouble. Good on you for noticing that and raising the question.
One more thing: yes, electron flow is negative to positive, which, confusingly, is opposite of what is called conventional current flow, which is positive to negative. It’s historical, because our understanding of electron theory came many decades after basic electricity. Blame Ben Franklin.
But know that when you’re talking about electricity, it’s overwhelmingly the ‘conventional’ current flows positive-to-negative notation that’s used. But if you prefer, Falstad lets you choose electron flow instead of ‘conventional’.
The confusion is in the schematic. V really means its connected to a voltage source, like the one shown below, it could be a battery or a power supply or whatever. It's understood that the voltage source is connected to ground. Below are two circuits that are the same thing but with different notation.
simulate this circuit – Schematic created using CircuitLab The unfortunate thing is they author really should have defined a better voltage source other than "V". The current flows from V to ground.
