So I'm reading "Elements of Computing Systems" trying to really understand how everything works underneath (Any other book/article suggestions that would help would be amazing) Since eventually I want to implement this basic stuff on a breadboard and maybe someday get a 4-bit computer or something similar going (but that's a while away).

Anyways I'm looking at the Section on Sequential Logic, and I guess I'm getting mixed up in the "time" or clock when it comes to registers and flip flops. When I think of flip flops I think of the Schematic such as this:

enter image description here

So I'm a bit confused when it says out(t) = in(t-1). For that matter, how exactly is a 0 represented in this case. I know 1 is a voltage being sent, but how would something like a Register holding 1 or 0 know how to differentiate the time difference in the signal being sent?

I'm also a bit confused by the 1-bit Register part, Is it saying that if there is a load that is being "sent down the line" that the output is the same as that load (I'm assuming load is equal to 1 or a current being sent)


as you can tell im a bit confused, I'm sorry if I'm all over the place, but I think it's the "clock" that's throwing me off.


There are flip-flops and there are flip-flops.

The RTL (resistor-transistor logic) schematic you show is a simple bistable multivibrator that is either set or reset by pulses on the E1 and E2 inputs. For exmaple, pulsing E1 high will cause A1 to go low and A2 to go high.

"Elements of Computing Systems" is talking about a different kind of flip-flop: the master-slave edge-triggered flip-flop. Rather than being driven by pulses, this kind of flip-flop reacts to the rising edge of a (typically) square-wave clock signal. The output of the flip-flop immediately after such a clock edge matches the input right before that same clock edge. This is where the t and t-1 notation comes from.

In its easiest to understand form, the D-type master-slave flip-flop consists of eight NAND gates (or eight NOR gates in RTL) and two inverters. As you might guess, this gets cumbersome to draw as a schematic using resistors and transistors. It's much easier to draw the schematic for one gate, and then use a symbol to represent that logical function in higher-order structures.

However, in the days when computers were really built using discrete transistors, master-slave logic was relatively rare. Instead, multi-phase clocks were generated so that the simpler pulse-driven flip-flops could be used, keeping the overall circuit complexity down.

  • \$\begingroup\$ It's worthwhile to note that when using discrete parts, capacitors can be used to obtain edge-triggered behavior without having to use transistor-based master/slave storage elements. Using capacitors in this way may limit the speeds at which devices can operate (a device with a rising-edge clock may require a significant setup time during which the data is valid and the clock low, before the rising edge), but using two caps, two transistors, and two diodes, may be preferable to having to use more transistors. \$\endgroup\$ – supercat Dec 14 '12 at 19:36

Think of the "t' above as the clock NUMBER. i.e. after 3,453 clocks the output will be in a "1" state. so therefore 't+1" = clock number 3454.

That statement for the output basically says the output after a given clock is the same as what was presented on the input after the previous clock.

It's a confusing mix up between discrete and continuous variables.


The book CODE: The hidden language of computer hardware and software is a great book that starts with the basics of how a transistor works and builds up to explaining an entire computer system. I highly recommend it. It sounds like exactly what you are trying to learn about. Hope this helps!


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