We will talk about the NOR gate.
While constructing the 6 gates using NOR gate,
the trick is to remember which gate to construct first and last
We will start with the NOT gate.
Let’s recap the truth table for NOR gate.
NOR gate produces an inverted output for these two
input combinations. Here, both the output are at the same logic level.
So we will short the two inputs of NOR gate.
When the input is at logic 0, the output is 1 and vice versa.
This is NOT gate constructed using a single NOR gate.
The second gate we would construct is an OR gate from NOR gate.
Now this is simple. If you complement the output of NOR gate,
we get an OR gate. Thus, we connect a single input NOR gate.
We have done it using 2 gates
NOR gate has the boolean expression A OR B bar (A+B BAR) where A and B are the
two inputs. However, if the two inputs A B are followed by a NOR gate, we get A bar and
B bar. These two outputs will be connected to a NOR gate, the boolean expression is A
bar OR B bar and the whole term inverted (A bar+B bar bar). If we apply Demorgan's theorem
to it, the output is A AND B which is the logical expression for an AND gate. We have
used 3 NOR gates for this.
If you complement the output of AND gate, we get a NAND gate.
Thus, a nand gate is obtained using 4 NOR gates.
The fifth gate we will construct is
an XNOR gate. If you recollect the XNOR expression, it is A XNOR B and it can also be expanded
this way that is A AND B OR A BAR AND B BAR.
Let's take the AND gate
constructed using NOR gates and connect one more NOR gate ahead. Pause the video and try
to solve this.
It gives the logical expression of an XNOR gate.
The last gate is an XOR gate.
It is obtained by inverting the output of an XNOR gate
i.e. by connecting one more nor gate.