When I first met the exotic RTL gate (see the attached picture), I was amazed since I could not imagine how it was possible humble ohmic resistors to perform logic operations. Until then I knew that logic operations were realized only with electrical switching elements – diodes, tubes and transistors. For example, if we had to realize a 2-input OR gate, I thought we should connect two diodes (transistors) in parallel to the input as it was made in the diode OR gate (see the link below). Instead two resistors were connected in the RTL gate. What was this absurdity?
https://en.wikipedia.org/wiki/Diode_logic#OR_logic_gate
Then I began asking myself a series of fundamental questions: “How can we implement basic Boolean functions? How can we materialize abstract binary logic functions in a form of electronic circuits? How do we make logic gates at all? What should they contain?” Here are my speculations...
YES/NOT. Simplest one-variable YES and NOT logic functions are realized by (non-inverting and inverting) threshold switching elements (comparators). These gates “need” the threshold to “classify” the input signal as HIGH (1) or LOW (0); for example, in the case of BJT gates, the forward voltage Vbe0 (about 0,7 V for Si transistors) usually serves as such a threshold.
OR/AND. These multivariable logic functions can be realized as an extension of the elementary one-variable YES and NOT functions where an arithmetical “summation” operation is added before the basic “comparison”. So the elementary logic functions OR/AND could be implemented by cascading two devices – a “summer” (a pure analog device) and a “comparator” (a mixed analog-to-digital device).
To realize an OR gate, the input variables should turn on (at logic "1") or turn off (at logic "0") equal reference quantities, and the comparator threshold should be lower than the magnitude of one reference (in the case of AND gate, the threshold should be somewhere between “n-1” and “n” references what is difficult to implement; IMO that’s why the first RTL gate was OR type). They are summed by the analog summer and their sum is compared by the threshold device (the comparator). Thus it is sufficient that only one reference quantity is turned on to set the output at logic "1", i.e. this “arithmetical” device performs... a logic OR function!
RTL. Historically maybe this was the first (arithmetical!) way to implement an electrical logic gate operating with voltages (there is evidence that RTL elements of this type have been used by John Atanasov in the first computer). Let's see how likely it happened...
A voltage summer can be implemented as series (KVL) or parallel (KCL). The disadvantage of the series summer is that the input sources (without one) should be "floating "; so, I suppose, that’s why a parallel voltage summer is used in the first RTL OR-NOT element (see the attached picture). The base resistors form a parallel voltage summer with equal weighted inputs (R3 = R4) and the common-emitter transistor stage acts as a threshold element with a threshold about 0,7 V. The resistances of the basic resistors are chosen so that it is sufficient to apply a voltage only at the one of the inputs (input logic "1") to obtain a sufficient voltage (> 0,7 V) for saturating the transistor and its collector voltage to become equal to zero (output logic "0"). Only if all input voltages are equal to zero (input logic "0s") , the transistor is cut-off and the output voltage is high (output logic "1") .
I suppose the third resistor R1 connected to the negative supply was then necessary because of using germanium transistors; it introduced an additional (negative, “pulling-down”) input to the summer...
I told this fancy story, three years ago, in the Wikipedia page about RTL:
https://en.wikipedia.org/wiki/Resistor%E2%80%93transistor_logic#One-transistor_RTL_NOR_gate
It is interesting to see if there is some connection between this RTL "arithmetical" idea and the "pure logic" idea of DL, DTL, TTL...
https://www.researchgate.net/post/What_is_the_basic_idea_of_the_input_logical_part_of_transistor-transistor_TTL_diode-transistor_DTL_and_diode_DL_logic_gates_Are_they_related
... ECL, CMOS... and maybe some other logic gate implementations? Or maybe they are all subject to this universal idea?
To make the discussion more interesting and exciting for yong people learning digital electronics, I would like to tell you how my students reacted when I suggested to them to join our RG discussions...
https://www.researchgate.net/post/I_intend_incorporating_my_students_during_the_labs_on_Digital_circuits_in_our_discussions_Do_you_have_something_against_Will_you_support_me_or_not
... It was on Monday... The next day, one of them - Lubomir, came to me and asked me to help him understand basic (digital) transistor circuits. I decided to do this by making him reinvent the first logic gate - RTL... and imagine this was continuing four hours! Here are the main steps of our "brainstorming" (I will first place a series of pictures and then will add some comments extracted from my voice recorder)...
We begin with considering the Wikipedia page about RTL...
http://www.researchgate.net/go.Deref.html?url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FResistor%25E2%2580%2593transistor_logic%23One-transistor_RTL_NOR_gate
CYRIL: What is the function of the transistor here? An amplifying element? Not only... We can think of it as of a threshold (0.7 V) switching device... look at its IV input curve to see the threshold...
LUBOMIR: So, when the voltage of the common point (where R3, R4, R1 and the base are joined) exceeds 0.7 V, the transistor saturates and the output voltage becomes zero?
CYRIL: Exactly! But how does this voltage depend on the input voltages? The links below can help us to answer this question:
https://en.wikibooks.org/wiki/Circuit_Idea/Parallel_Voltage_Summer
https://en.wikibooks.org/wiki/Circuit_Idea/Walking_along_the_Resistive_Film#Varying_both_V1_and_V2:_a_resistive_summer
CYRIL: So, R3 and R4 form a parallel (why?) voltage summer with weighted inputs. We can investigate its operation in an attractive way, if we visualize the invisible electrical quantities: voltages - by red bars; currents - by green loops:
http://www.circuit-fantasia.com/collections/circuit-collection/circuits/old-circuits/v-to-v-sum-old.html
CYRIL: To see the role of the "pulling-down" resistor R1, we can draw it and its negative voltage source below the ground. It is interesting that the two voltage sources are connected in series, in the same direction, so that their voltages are summed, right? Do you begin seeing the OR operation here? The two resistors R3 and R1 are...
LUBOMIR: ... "push-pull" and "pull-down" elements...
CYRIL: Exactly... If there was not such a resistor (R1), and both the input voltages were zero, the base voltage would be zero... what would be a problem in the case of a Germanium transistor... so the role of R1 is to reduce the base voltage below the ground... see where the current flows and where the red voltage bars are...
LUBOMIR: Yes, I see... this summer is a "3-input summer"; it sums two positive and one negative voltages...
CYRIL: But let's see how this passive resistive circuit is calculated - if there is only one input voltage, the base voltage should become positive and > 0.7 V... Only one voltage is sufficient (to obtain OR), right?
LUBOMIR: And where will the current flow then?
CYRIL: Until then, the current flows through the two sources and two resistors connected in series; thereafter the turned-on base-emitter junction diverts some current and the transistor saturates...
LUBOMIR: ... and the current finally returns to where it was started...
CYRIL: Yes, Lubomir... remember this circuit wisdom: each current returns to where it started...
It's time to put in practice this idea. We use an Si transistor; so there is no need of R1 and the negative supply; the threshold is about 0.7 V. To visualize the output, let's connect a LED in series to the collector resistor (only note it will light when the output is at logic "0"). Now, if we connect the positive rail to R3 or R4 or the both, the LED lights.
But the humble LED has also a threshold (about 2 V if it is red)... So, we can make a small "invention" using only the LED as a threshold device (instead a transistor, collector resistor and a LED). This will be another logic "family" - RLED:) in addition to RT, DT and TT families...
The first logic gates were electromechanical relays. Dating back to the early 20th century. Full blown stored program computers were built using them. Here is a letter from John Von-Neumann to J. Robert Oppenheimer during the Manhattan Project on what relay based computer to buy. A fascinating read on early computers. A relay is also a threshold device. The pull in voltage is the logic threshold. The contacts can be arranged in any AND/OR configuration. By the mid 1940's vacuum tubes were brought on as the logic elements. The late 1950's saw both tubes and transistors used in computers. The Noyce idea of IC's was simply the realization that the same processes used to make planar transistors could be expanded to more complex complete circuits.
http://www.tminus7.com/John_von-Neumann.pdf
Your: "It is interesting to see if there is some connection between this RTL "arithmetical" idea and the "pure logic" idea of DL, DTL, TTL..." is not a good way of looking at this. All logic gates ARE analog devices in nature. In fact logic gates with feedback are used to make clock oscillators all the time. Even on the most modern chips this is done.
What distinguishes a logic gate from a simple analog amplifier is the gain. The input/output voltage ratio. Logic gates are designed to go "hard over" above or below their threshold level. They saturate to full supply or to zero volts, depending on if they are above or below the threshold.
Remarkable thoughts... I like them... In the laboratoy, I do а historical trip with my students through the years (switch -> relay -> tube -> diode -> BJT -> MOS --->>> generalized switching element). Excluding the 2-terminal diodes, the rest elements (4-terminal or 2-terminal with a common terminal) are intuitive and comprehensible. I try very endeavor to explain to my students how a diode can act as a switch (how to drive it with a grounded input voltage):
https://www.researchgate.net/post/What_is_the_basic_idea_of_the_input_logical_part_of_transistor-transistor_TTL_diode-transistor_DTL_and_diode_DL_logic_gates_Are_they_related
I always begin with the "relay analogy" but they (students from the Computer Systems department) have no clear idea about it:) This situation is a good example of how an analogy may be useful for one and useless for another (it depends on the previous experience)...
Thank you for the participation and especially for the remarkable Neumann's work. Cyril
So there are not digital circuits; they are analog circuits made act (forced, overloaded) as digital ones; digital circuits are modified analog circuits... Two days ago, I said it to my students because I had somehow to explain to them why it was necessary to measure the transfer (analog) characteristic of the digital TTL logic gate...
About the hypothetical connection between logic families... I mean if we can see some arithmetical summation (like in the input part of RTL) in all these logic gates (DL, DTL, TTL, CMOS)...
use two diodes and supply for two input and one output logic gate truth table. or Simply use only two switches with supply. For OR gate put them in parallel, for AND in Series and for NO T use single switch. Similarly diodes can be used instead of switches
But there is something surprising here - both the diode configurations are parallel:
https://www.researchgate.net/post/What_is_the_basic_idea_of_the_input_logical_part_of_transistor-transistor_TTL_diode-transistor_DTL_and_diode_DL_logic_gates_Are_they_related
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