Final answer:
The minimum SOP form of the given expression ĆBĆCĆ + ĆBĆC + ABC using a Karnaugh map is ĆBĆ + ABC. It is found by placing the expressions into the K-map, looking for groups of 1s, and simplifying. The terms are then eliminated, resulting in a simplified and reasonable algebraic expression.
Step-by-step explanation:
To find the minimum Sum of Products (SOP) form using a Karnaugh map for the given expressions, we need to place the expressions in standard form and map them onto the K-map. The given expressions are ĆBĆCĆ + ĆBĆC + ABC. We can draw a 3-variable Karnaugh map, and fill in the minterms based on the expressions. A '1' goes in the cell for ABC (111), and ĆBĆC (001) and its adjacent cell for ĆBĆCĆ (000). Once we place the 1s, we look for groups of 1s that can be combined to simplify the expression.
The grouping results in two groups, one for the terms ĆBĆCĆ and ĆBĆC which simplifies to ĆBĆ, and one for the single term ABC. Thus, the minimum SOP form of the given expression is ĆBĆ + ABC.
We then eliminate terms wherever possible to simplify the algebra. Our final SOP expression has been simplified such that it cannot be reduced further, which makes it reasonable based on Karnaugh map simplification rules.