as discussed previously transistors are the most basic elements of digital circuits and systems so transistors basically work as switches and these switches can be used to represent digital signals the most common building blocks in digital systems are Gates or more specifically logic gates so there are three three basic Gates using which you can construct most digital systems basically all the digital systems you find today are constructed using the three basic Gates the first gate is the and gate so this is the circuit level description of an and gate it is just for your understanding so let's say I have a battery here it's connected to the ground this is my switch a this is switch B so right now both my switches are off basically uh switches off indicates that it's like this and a switch on indicates that it's like this at the end of the two switches I have a bulb which close it can be an LED or any any other bulb and I close the circuit now what are the conditions of switch a and switch B for the bulb to Glow so a b let's say the bulb is f now there are four different combinations in which switch a and switch B can be positioned the first combination is switch a is on the first combination is both switches are off the second combination is switch a is off but switch B is on the third combination is switch a is on but B is off and the last combination is both my switches are on so for which combination do you think the bulb will glow so for what combination of A and B will my bulb glow bulb glowing in the sense one is bulb is on and zero is BU bulb off so when both my switches are off there is no way that the current is going into the bulb which means that my bulb is off now when switch a is off and switch B is on the current is not going to go through because switch a is off therefore my current does not reach my bulb so it's still not it still doesn't glow same thing happens when switch a is on and switch B is off the current passes through switch a but it gets blocked by switch B therefore no current goes through the bulb therefore it's off and then finally when both my switches are on that is when my circuit is complete and my bulb Clos so this is the true table so this operation is is nothing but the operation of an and gate and it is represented as so if so this is the gate A and B are the inputs to the gate and F is the output to the gate now f is asserted that is the output of the and gate is asserted when both A and B are asserted that is for this combination here so this is the symbol representation of the gate and the mathematical description is f equals A and B some people also write f equals A and B they do not include the dot but it's implied and some people write f equals to A and B I typically use one of these two they are interchangeable that's no problem and a and b this is used in vhdl programming uh we're going to deal with that later but throughout the course when I mean a It Means A and B the second gate is the orgate so let's look at the high level description of the orgate so you have have a battery here which which is connected to the ground this is switch a this is switch B and here's my bulb F and I Conn connected back to the ground again similar to your and gate there are four combinations so both switches can be off one of them can be on and the other one can be off and both switches are on so for what combinations of A and B do you think the bulb will glow so if both my switches are off then the current is not going to go through any of the switches and it's not going to reach the bulb so the bulb remains off when at least one of the switches is open let's say in this case switch B is open or switch B is on then my current is going to go through this direction here and it reaches the bulb so it's going to be one on uh the same thing happens when switch a is on but switch B is off in that case current will directly go from here all the way to the bulb so that's the bulb is on and when both the switches are on the current goes through both of them and it's going to come out of here and reach the bulb so that's one so for an orgate if at least one of the inputs is one then your output is a one so the symbol for the argate is so if at if at least so if at least one of the input is asserted the output is asserted the mathematical description of the orgate is f equals A or B and some people write fals a or b but I'm going to use this notation the final gate that we're going to deal with is the not gate it's also known as the inverter so what a not gate does is you have an input a this is the symbol of the no gate and you have F so the true table is a can take either Z or one so when a is a zero your not gate is going to flip the out uh flip the input so if a is zero your output is one and if your a is 1 your output is zero and they typically write f equals not a some people use a bar some people use a prime I typically use these two so using these three gates all modern digital systems are designed the most complex processor is going to contain these three gates there are other Gates as well but those Gates can be constructed using these three gates