Implement XOR Gate using 2x1 Multiplexer

We have two inputs A, B. Connect one of Multiplexer's input to input 'B'. Connect input 'B' to input of NOT gate and output of this NOT gate connect to second input of Multiplexer. Then connect input 'A' to selection line of Multiplexer. So, this Multiplexer will XORing operation of input A, B.

Implement OR Gate using 2x1 Multiplexer

We have two inputs A, B. Connect one of Mux's input to logic '1' and second to input 'B'. Connect input 'A' to selection line of Mux. So, output will give ORing operation of two inputs A, B.

Implement AND Gate using 2x1 Multiplexer

We have two inputs A, B. Connect one of Mux's input to logic '0' and second to input 'B'. Connect input A to selection line of Mux. So, output of Mux will give anding operation of two inputs A and B.

Implement BUFFER Gate using XOR Gate

Connect one of XOR gate's input to logic '0' and connect second to input 'a'. So XOR gate will give output as input.

Implement NOT Gate using XOR Gate

Connect one of XOR gate's input to logic 1 and connect second input to input 'a'. So output of XOR gate will give inverted output of input.