Hello dear followers! Welcome to a new article where we will simplify one of the most common Boolean algebraic expressions - the Sum of Products (SOP) form, also known as the canonical form.
Step 1: Identifying Common Factors
In Boolean algebra simplification problems like this one, we always begin by identifying common factors among the expression terms. The first step in our Boolean minimization process is to rearrange and group terms that share common variables, making the factoring process more systematic and error-free.
Step 2: Initial Factorization
Following the identification of common literals in our Boolean expression terms, we initiate the factorization procedure. This essential Boolean algebra technique yields the following intermediate result:
Step 3: Analyzing Parenthetical Expressions
Following the Boolean algebra factoring phase, we concentrate on the expressions remaining within the parentheses. Analyzing our grouped terms, we observe that the first two parenthetical expressions contain the XOR (exclusive OR) operation between variables C and D. Meanwhile, the last parenthetical expression reveals the complement law application: C + C̅ = 1, which represents a fundamental Boolean algebra identity.
Step 4: Substitution and Further Simplification
Following the substitution step in our Boolean algebra simplification process, we first examine whether any Boolean algebra rules or theorems can be applied directly to further reduce the expression. Next, we search for new common factors among the remaining terms or consider algebraic expansion if it leads to simplification. In this particular Boolean minimization problem, we identify C⊕D (XOR of C and D) as a common factor. After factoring this out, we discover that the expression inside the parentheses simplifies to A⊕B (XOR of A and B).
🎯 Final Simplified Expression
Consequently, our Boolean expression transforms into the following optimized form:
F = (C ⊕ D)(A ⊕ B) + ABD
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