How many gate(s) would be required to implement the following Boolean…
2018
How many gate(s) would be required to implement the following Boolean expression after simplification?
- A.
1
- B.
2
- C.
3
- D.
4
Attempted by 350 students.
Show answer & explanation
Correct answer: A
Simplified solution and gate count:
Factor the common term with C̅: (C̅D̅ + C̅D) = C̅(D̅ + D) = C̅.
Substitute into the expression to get Ā·C̅ + A·C̅·(B + B̅).
Use (B + B̅) = 1 to simplify to Ā·C̅ + A·C̅.
Factor C̅: C̅(Ā + A) = C̅·1 = C̅.
Final simplified expression: C̅.
Implementation gate count: only one NOT (inverter) gate is required to produce C̅.