Diode Logic Gates
All you have to remember, is that current flows through a diode in the direction of the arrow.
In the case of the OR gate, if there is no potential (i.e. logic 0, or ground) on both inputs, no current will pass through either diode, and the pull-down resistor R\$_{L}\$ will keep the output at ground (logic 0).
If either of the inputs has a positive (logic 1) voltage on its input (In 1 or 2), then current will pass through the diode(s) and appear on the output Out, less the forward voltage of the diode (aka diode drop).
The AND gate looks more challenging because of the reversed diodes, but its not.
If either input (In 1 or In 2) is at ground potential (logic 0), then due to the higher potential on the anode side due to the positive voltage from resistor R\$_{L}\$, current will flow through the diode(s) and the voltage on the output Out will be equal to the forward voltage of the diode, 0.7v.
If both inputs to the AND gate are high (logic 1), then no current will pass through either diode, and the positive voltage through R\$_{L}\$ will appear on the output Out.
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As an aside, diode logic by itself is not very practical. As noted in the description of the OR gate for example, the voltage on the Out terminal when there is a logic high (1) on either of the inputs will be the voltage on the input minus a diode drop. This voltage drop cannot be recovered using just passive circuits, so this severely limits the number of gates that can be cascaded.
With diode logic, it is also difficult to build any gates other than AND and OR. NOT gates are not possible.
So enter DTL (diode transistor logic), which adds an NPN transistor to the output of the gates described above. This turns them into NAND and NOR gates, either of which can be used to create any other kind of logic function.
Sometimes a combination of diode logic and DTL will be used together; diode logic for its simplicity, and DTL to provide negation and regeneration of signal levels. The guidance computer for the Minuteman II missile, developed in the early 1960's, used a combination of diode logic and diode transistor logic contained in early integrated circuits made by Texas Instruments.
You can understand easily understand logic circuits made from diodes by considering ideal model of a diode in which we ignore 0.6-0.7v in-built forward voltage drop of a diode, any bulk resistance and non-idealities. So basically we consider ideal diode as a perfect switch: it is closed when forward biased and open when reverse biased
Ideal Diode Model
Vp = voltage at P or Anode terminal of diode
Vn = voltage at N or Cathode terminal of diode
Vpn = Vp - Vn = terminal voltage across diode
Id = current through diode
if Vpn < 0, Diode is reverse biased and acts as an open circuit i.e. Id = 0
if Id != 0, Diode is forward biased and acts as a short circuit i.e. Vpn = 0
Using this model, lets calculate current I through through resistor
OR Gate
In1 In2 I Out
0v 0v 0 0v
0v Es Es/R Es
Es 0v Es/R Es
Es Es Es/R Es
Whenever atleast one of the two inputs is held to high (Es), a non-zero current flows towards the ground through the resistor as respective diode is forward biased and acts as short circuit. As voltage drop across a diode acting as a short circuit is 0, therefore terminal Out is held to input high (Es). When both inputs are held to ground (0v), both diodes are reverse biased and hence open circuited and no current flows through resistor. As a result, terminal Out is now held to ground (0v)
AND Gate
In1 In2 I Out
0v 0v Es/R 0v
0v Es Es/R 0v
Es 0v Es/R 0v
Es Es 0 Es
Whenever atleast one of the two input terminals is held to ground (0v), their respective diode is forward biased and acts as short circuit causing non-zero current to flow through the resistor. As voltage drop across a diode acting as a short circuit is 0, therefore terminal Out is held to ground (0v). When both inputs are held high (Es), now both diodes are reverse biased and thus act as open circuits and no current flows through the resistor. As a result, terminal Out is now pulled to high (Es)