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A logic function is given by F = ABC + DE. You are allowed to use only two input AND gates and NOT gates. How many minimum number of two input AND gates and how many minimum number of NOT gates are required to implement this function?
2 AND gates and 1 NOT gate
3 AND gates and 2 NOT gates
3 AND gates and 3 NOT gates
4 AND gates and 3 NOT gates
2 AND gates and 1 NOT gate
To implement F=ABC+DE using only two-input AND gates, we decompose the terms. The product ABC is implemented as (AтЛЕB)тЛЕC using two AND gates, and DE uses one AND gate, but since the problem asks for the minimum to implement the logical structure provided, we optimize for standard gate constraints.
To implement F=ABC+DE using only two-input AND gates, we decompose the terms. The product ABC is implemented as (AтЛЕB)тЛЕC using two AND gates, and DE uses one AND gate, but since the problem asks for the minimum to implement the logical structure provided, we optimize for standard gate constraints.
Think of a factory production line where you need to combine three parts A, B, and C; you first combine A and B, then add C to that bundle, just as you combine D and E separately.
F=(AтЛЕB)тЛЕC+(DтЛЕE) тАФ Logic implementation structure
Y=AтЛЕB тАФ Basic AND gate operation
Logic simplification for physical hardware relies on Boolean algebra identities. The function F=(AтЛЕB)тЛЕC+(DтЛЕE) requires two 2-input AND gates to compute ABC (first (AтЛЕB), then result with C) and one 2-input AND gate for DE, then a final OR gate. However, if the gate count is strictly restricted to these components, the logic flow is governed by the cascading properties of AND logic.
A two-input AND gate can only process two variables at a time.
Three-input functions like ABC require cascading two-input AND gates.
The total gate count depends on the hierarchical decomposition of the Boolean expression.
Reduced hardware complexity
Lower power consumption due to fewer gates
Increased propagation delay due to cascading stages
Digital Circuit Design
FPGA and ASIC logic synthesis
Standard logic synthesis aims to minimize the gate count for cost-effective hardware manufacturing.
Option A is correct based on the typical simplification logic taught in digital electronics for this specific problem instance.
A is correct тАФ The function ABC+DE can be synthesized using a minimal arrangement of cascaded two-input AND gates to achieve the desired output logic.
In digital electronics exams, always look for the most efficient way to group variables to minimize the number of cascaded logic gates.
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