The XNOR Gate:
The logic symbol is the same as the XOR gate with an inversion bubble placed at the output side. The exclusive NOR gate produces an inverted output as that of the XOR gate.
Learning Objectives:
Working:
Case 1:
Input A = 0
Input B = 0
Output = 1
Case 2:
Input A = 0
Input B = 1
Output = 0
Case 3:
Input A = 1
Input B = 0
Output = 0
Case 4:
Input A = 1
Input B = 1
Output = 1

2 Input XNOR Gate |
Input A | Input B | Output |
0 | 0 | 1 |
1 | 0 | 0 |
0 | 1 | 0 |
1 | 1 | 1 |

Logical Expression:
Y = A + B
Logical XNOR Gate (Explain with the help of switches)
The XNOR switch model contains 4 switches. Switch A and its complement switch AC. Similarly, there is a switch B and its complement switch BC. Output goes high when both inputs are either zero or high. The switch circuit fulfils both conditions. When switch A and switch B are closed (logic 1), output goes high. Similarly, when switch A and switch B are opened (logic 0) the complement switches AC and BC are logic high. Output goes high in this case as well.
Implementation Using Diode Logic

The XNOR gate diode (DTL) circuit was not an easy task. I tried many different ways but I failed. Finally, I draw a schematic that contains a transistor at the end of the bridge circuit. It performs an inversion operation. The whole circuit is similar to the XOR diode circuit except for the last transistor.
Case 1:
Look at the schematic in case 1. Both switches are open. All diodes remain turned off. The transistor is also turned off. Output (LED is turned on) is high.
Case 2:
In this case, switch S1 is connected to a 5V source while S2 remains connected to the ground. S1 is connected to the diode D1, and D1 is connected to the transistor Q1. It turns on Q1. No current flows from the LED and hence the output is low.
Case 3:
Same as case 2.
Case 4:
Look at the schematic in case 4. Switches S1 and S2 are connected to 5V sources. S1 turns on D1 and S2 turns on D2. Look at node 2. There is no potential difference at this node and hence no current will flow from this path. No current will flow to the base of Q1 and transistor Q1 will remain turned off. Output goes high.
Implementation Using Transistor Logic

It is surprisingly easy to design a BJT based XNOR gate. It only contains two BJT transistors. Collectors are connected. Bases are connected to the 5V source via switches S1 and S2. The emitter of Q1 is connected to S2 and the emitter of Q2 is connected to S1. The configuration is the same as that of the XOR gate. The only difference is the third Transistor which performs inversion operation (in the case of the XOR gate).
Case 1:
Look at the schematic, both switches S1 and S2 are open. Both transistors are off. No current will flow from the transistors. The output will be high.
Case 2:
In this case, switch S1 is connected to a 5V source. The base of Q1 is connected to S1 and the emitter of Q1 is connected to S2 which is grounded. Transistor Q1 is on and all the current flows through Q1. Output remains low.
Case 3:
Same as case 2.
Case 4:
Look at the schematic in case 4. Both switches S1 and S2 are connected to 5V sources. The base of Q1 is connected to V1 and the emitter of Q1 is connected to V2. So, the is no potential difference between base and emitter and hence
VBE = 0
Similarly, this is true for Q2. Both transistors are off. And hence output goes high.
The XNOR Gate | BJT XNOR Gate | Diode XNOR Gate