Digital Logic

Step 1: Identify Logic Gates in the Circuit
The circuit consists of:
- An OR gate taking inputs

A

and

B

.
- An AND gate taking inputs

A

and

B

.
- The outputs of these gates are passed through another OR gate.
Step 2: Derive Boolean Expression The intermediate outputs are:

X%20%3D%20A%20%2B%20B%20%5Cquad%20%5Ctext%7B(OR%20gate)%7D

Z%20%3D%20A%20%5Ccdot%20B%20%5Cquad%20%5Ctext%7B(AND%20gate)%7D

The final output

Y

is obtained as:

Y%20%3D%20X%20%2B%20Z%20%3D%20(A%20%2B%20B)%20%2B%20(A%20%5Ccdot%20B)

Using Boolean algebra:

Y%20%3D%20A%20%2B%20B

Step 3: Construct Truth Table

%5Cbegin%7Barray%7D%7B%7Cc%7Cc%7Cc%7C%7D%0A%5Chline%0AA%20%26%20B%20%26%20Y%20%5C%5C%0A%5Chline%0A0%20%26%200%20%26%200%20%5C%5C%0A0%20%26%201%20%26%201%20%5C%5C%0A1%20%26%200%20%26%201%20%5C%5C%0A1%20%26%201%20%26%201%20%5C%5C%0A%5Chline%0A%5Cend%7Barray%7D

Final Answer: The correct truth table matches option (3).

Chapter Questions
2 MCQs