Ncert Exercises & Solutions

An X-OR gate has following truth table.

It is represented by following logic relation $Y = \bar{A} . B + A . \bar{B}$

Build this gate using AND, OR and NOT gates.

Hint: The logic circuit can be obtained using two NOT gates.

Step 1: Find the logic circuit for

Y_{1}

and

Y_{2}

Given, the logic relation for the given truth table is,

Y = \bar{A} . B + A . \bar{B} = Y_{1} + Y_{2}

when Y_{1} = \bar{A} . B and Y_{2} = A . \bar{B}

Y_{1}

can be obtained as output of AND gate I for which one input is of A through NOT gate and another input is of B.

Y_{2}

can be obtained as output of AND gate II for which one input is of A and other input is of B through NOT gate.

Step 2: Find the logic circuit for Y.

Now

Y

can be obtained as output from OR gate, where,

Y_{1}

and

Y_{2}

are input of OR gate.

Thus, the given table can be obtained from the logic circuit given below.