Sigma and Pi Notation
Hardware engineers rely on compact mathematical notations to document large logic functions before synthesis. The circuit behavior is fully defined by mapping active and inactive states to decimal indices.
A four-variable Boolean function is defined using standard sum-of-minterms notation as F(A, B, C, D) = Σm(0, 3, 7, 9, 14).
Determine the full canonical Sum of Products (SOP) expression and its Product of Sums (POS) equivalent. Expand the decimal indices directly into their four-variable binary representations to identify the constituent logic terms.
Constraints
- Variables are strictly ordered from Most Significant Bit (
A) to Least Significant Bit (D). - Minterms use standard binary weighting.
- The function scope is exactly four variables, establishing a fixed upper bound of 16 possible states.
Topics
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