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A logic function is given by F = (A + B) тЛЕ(C+D).Using only two-input OR gates and two-input AND gates, what is the minimum number of gates required to implement this function?
Two OR gates and one AND gate
One OR gate and two AND gates
Three OR gates and one AND gate
Two OR gates and two AND gates
Two OR gates and one AND gate
To implement the function F=(A+B)тЛЕ(C+D), we require two OR gates to compute the terms (A+B) and (C+D) separately. These intermediate results are then fed into a single two-input AND gate to produce the final output F.
To implement the function F=(A+B)тЛЕ(C+D), we require two OR gates to compute the terms (A+B) and (C+D) separately. These intermediate results are then fed into a single two-input AND gate to produce the final output F.
F=(A+B)тЛЕ(C+D) тАФ Boolean representation of the logic function.
The expression consists of two Boolean sums that act as inputs to a final product operation. Since the gate constraints are restricted to two-input logic gates, the expression can be evaluated directly by mapping each addition operator to an OR gate and the multiplication operator to an AND gate.
OR gates are used for the summation of input variables A+B and C+D.
The AND gate performs the logical conjunction of the two OR-gate outputs.
Total gate count = 2 OR gates + 1 AND gate = 3 gates.
Minimal gate count optimizes hardware footprint.
Reduction in propagation delay compared to complex gate structures.
Specific to the provided two-input constraint.
Does not account for gate propagation delays or fan-out capabilities.
Implementation of basic Sum-of-Products or Product-of-Sums expressions.
Digital logic circuit design optimization.
Option B (one OR and two AND) is incorrect as it would imply a function of three terms or different logic flow.
Option C (three OR and one AND) suggests more components than required for the given expression.
Option D (two OR and two AND) is redundant for this specific expression.
A is correct тАФ The implementation requires exactly two OR gates for the sums and one AND gate for the product of those sums.
Always break down the Boolean expression into basic operations. In exams, look for the lowest number of operators first before checking gate availability constraints.