### 2-Input NOR Gate using 2:1 Multiplexer - Basic Gates design using MUX

Using Multiplexer any combinational logic circuit can be designed. Here you would see how to implement a 2-input  NOR gate using a 2:1 multiplexer - Basic Gates design using MUX

## 2-Input NOR Gate using 2:1 Multiplexer - Basic Gates design using MUX

### Step 1: To write the Boolean function of the gate to be designed

Here a 2-input NOR gate is to be designed using a 2:1 Multiplexer.

Truth table of 2-input NOR gate is:

 A B Y 0 0 1 0 1 0 1 0 0 1 1 0

Therefore, Boolean Function of NOR Gate would be

Y(A, B) = Σm(0)

### Step 2: To find number of select lines and input lines of the Multiplexer

For n variable Boolean function, the number of select lines of multiplexer (MUX) would be (n-1).

As we know that for a 2:1 MUX number of select lines would be 1. In this case there are two variables A & B.

i.e., n = 2

Therefore, Number of select lines would be n-1 = 1.

The variable B (LSB) would be used as select lines.

And variable A, which is the MSB, would be taken as the input variable.

### Step 3: Formation of Implementation Table

Write the MSB, i.e. A, at the left side of the table column wise and the other variable i.e., B at the top of the table row wise sequentially as shown below:

Write numbers from 0 to 3 in the cells of the implementation table.

Encircle the numbers or minterms given in the question.

If both the numbers in a column are encircled, then put ‘1’ against the corresponding input line ‘I’.

If both the numbers in a column are not encircled, then put ‘0’ against the corresponding input line ‘I’.

If only one number is encircled in a particular column, then write its corresponding MSB i.e., A or A/ against its input line ‘I’.

### Step 4: To draw the circuit for implementing 2-input NOR Gate using 2:1 MUX

As seen from the implementation table, to design a 2-input NOR Gate, connect the input I0 of the 2:1 multiplexer  to ‘A/  and the input I1 to the ground.

In this way a 2 input NOR Gate can be implemented using a 2:1 multiplexer.

Hope this post on "2-Input NOR Gate using 2:1 Multiplexer - Basic Gates design using MUX" would help in clearing many doubts in Multiplexer.