Fundamentals of Electronics -- 2

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Given a standard SOP (Sum of Products) expression, we're tasked with finding the binary values that make the expression equal to 1. However, you didn't provide a specific SOP expression, so I'll create a sample problem and walk you through the solution. Consider the following Boolean expression in SOP form: F(A, B, C) = A'B'C + AB'C' + ABC Here, we want to determine the binary values for A, B, and C such that the SOP expression equals 1. 1-A'B'C: This term is true when A=0, B=0, and C=1. Binary input: 001, Output: 1 2-AB'C': This term is true when A=1, B=0, and C=0. Binary input: 100, Output: 1 3-ABC: This term is true when A=1, B=1, and C=1. Binary input: 111, Output: 1 For the binary values 001, 100, and 111, the SOP expression equals 1. Now let's convert a given Boolean expression to SOP form: G(A, B, C) = (A + B)(A + C)(B' + C') Step 1: Apply the distributive law (FOIL): G(A, B, C) = (AA' + AC' + BA + BC + AB'C' + AC'B') Step 2: Simplify the expression by eliminating terms that simplify to 0 or are redundant: G(A, B, C) = (AC' + AB + BC + AB'C' + AC'B') This is the Boolean expression G(A, B, C) in SOP form.

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