Question

From the logic gate diagram given below:

1. Derive Boolean expression for (1), (2) and R. Reduce the derived expression.  [4]
2. Name the logic gate that represents the reduced expression.  [1]

Answer 1

1. The output of the first OR gate is (1) = A + B.
   This output is then inverted by the NOT gate, giving (1)' = (A + B)'.
   The expression for the second OR gate is (2) = A + B.
   The final AND gate receives inputs (1)' and (2).
   Thus, the resulting expression is:
   R = A + B • (A + B)
   Applying the absorption principle (where X•X' = 0), the value of R becomes 0, indicating that the output is always zero, regardless of the inputs.
2. The circuit is a grounded logic gate (always LOW) as the simplified equation shows a constant 0 function.