Physics · Logic gates (OR, AND, NOT, NAND and NOR)
The minimum number of gates required to realise the expression is
The minimum number of gates required to realise the expression \( Z= \) \( D A B C+D \overline{A B C} \) is
- A. One
- B. Two
- C. Eight
- D. Five
Step-by-step solution
The expression Z = D A B C + D \overline{A B C} simplifies to D because (ABC + \overline{ABC}) = 1, so Z = D. Thus, the function can be realized by simply connecting the input D to the output. However, if a gate is required, a single AND gate with one input tied to logic 1 (or a buffer) suffices. Therefore, the minimum number of gates is one.
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