Which one of the circuits given in the options correctly implements the Boolean expression:
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Which one of the circuits given in the options correctly implements the Boolean expression:
$$Y = AB' + C'D$$
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Answer: C. Circuit with upper AND gate AB', lower AND gate C'D, and OR gate
To implement the Boolean sum-of-products expression:
$$Y = AB' + C'D$$
First Product Term ($AB'$):
- Requires input $A$ fed directly into an AND gate.
- Input $B$ passed through an inverter (NOT gate) to form $B'$, which is fed into the same AND gate.
- Output of first AND gate: $AB'$.
Second Product Term ($C'D$):
- Requires input $C$ passed through an inverter (NOT gate) to form $C'$.
- Input $D$ fed directly into an AND gate.
- Output of second AND gate: $C'D$.
Sum Term ($+$):
- The two product terms $(AB')$ and $(C'D)$ must be fed into a 2-input OR gate.
- Final output: $Y = AB' + C'D$.
Inspecting the options:
- Option A feeds $B$ directly into the top AND gate without an inverter, giving $AB$, which is incorrect.
- Option B uses a NAND gate at the upper stage, giving $\overline{AB'}$, which is incorrect.
- Option C accurately feeds $A$ and $B'$ into an AND gate, $C'$ and $D$ into an AND gate, and combines their outputs via an OR gate, matching $AB' + C'D$.