✏️ Explanatory Question

[Computer Hardware]

Question:

Draw the logic circuit diagram for the simplified form of the following expression: 

AB'C + AB'C + ABC

The circuit diagram should only contain:

  • One AND gate
  • One OR gate
  • One NOT gate

Question Diagram:


Expression:

AB'C + AB'C + ABC

Answer:

Step 1: Simplification

AB'C + AB'C + ABC

= AB'C + ABC

= A(B'C + BC)

= AC

Simplified Expression:

AC

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← Previous [Computer Hardware] Question: Following is the circuit diagram of a Full Adder. Redraw the circuit diagram by adding the missing logic gates. Figure: Diagram of a full adder
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Answer with Explanation

answer circuit
Figure: answer circuit

Answer Diagram:

A ───────────────┐
                          │
                          ▼
                      ┌───────┐
                      │ AND   │──────► Output
                      └───────┘
                          ▲
                          │
         C ───────────────┘

Explanation:

  • Duplicate term: 
    AB'C
    is removed.
  • Common factor A is taken: 
    A(B'C + BC)
  • Using Boolean simplification: 
    B'C + BC = C
  • Final simplified expression: 
    AC
  • Therefore, only one AND gate is required.

Conclusion:

Simplified Expression = AC

The circuit uses:

  • One AND gate ✅

task for you

answer circuit
Figure: answer circuit
← Previous [Computer Hardware] Question: Following is the circuit diagram of a Full Adder. Redraw the circuit diagram by adding the missing logic gates. Figure: Diagram of a full adder