Question

Show how the circuit depicted in Figure 9.26 computes on input 0110 by showing the values computed by all of the gates, as we did in Figure 9.24.

Short answer

The final output is 0 because here even number of 1’s has taken (as the definition of parity function says).

Step-by-step solution

Step 1: Representation of the parity functional circuit

The n-input parityfunctionparity {0,1}ⁿ {0,1}gives an output 1 if an odd number of 1’s appear in the input variable and otherwise gives 0. The circuit depicted here (refer figure 9.26) is used as a parity functional circuit on four variable.

In this parity functional circuit, a number of gates are used. Therefore, first of all, the working of gates will be discussed here to understand the process performed in that circuit.

Step 2: The Truth table for and operator is as follows:

The following figure shows the how input and output can be taken in the above table (for and operator):

The Truth table for not operator is as follow:

The Truth table for not operator is as follow:

Input(x)	Output(z)
0 1	1 0

The following figure shows the how input and output can be taken in the above table (for not operator):

Step 4: The Truth table for or operator is as follow:

Input	Outputz
x	Y
0 0 1 1	0 1 0 1	0 1 1 1

The following figure shows the how input and output can be taken in the above table (for or operator):

Step 5: Consider the figure given below:

Above figure shows the functional parity circuit on 4 variables. Here 0110 is taken as an input variable. Now AND gate, OR gate and NOT gate applied on the input in the

Hence the final output is 0 because here even number of 1’s has taken (as the definition of parity function says).