Question

Find the truth table for the function Y of A and B represented in the following figure. 

 

• A. A
• B. B
• C. C
• D. D

Hint:

When a circuit's output doesn't match any options, simplify the Boolean expression first ($Y = (A \cdot B) + \overline{B} = A + \overline{B}$). If it still doesn't match, consider the possibility of a typo in the question diagram and check if the options match a basic logic gate's function (like OR, AND, etc.).

Answer 1

The Correct Option is C

From the given logic circuit: 
The upper gate is an AND gate with inputs $A$ and $B$. \[ \text{Output}_1 = A \cdot B \] 
The lower branch takes input $B$ through a NOT gate. \[ \text{Output}_2 = \overline{B} \] 
These two outputs are connected to an OR gate. 
Hence the output function is: \[ Y = (A \cdot B) + \overline{B} \] Now simplify using Boolean algebra: \[ (A \cdot B) + \overline{B} = (A + \overline{B})(B + \overline{B}) \] Since: \[ B + \overline{B} = 1 \] \[ Y = A + \overline{B} \] Truth Table for $Y = A + \overline{B}$