Final answer:
To derive a standard SOP expression, create a truth table and identify rows with a true output, and for each row create a product term. To derive a standard POS expression, create a truth table and identify rows with a false output, and for each row create a sum term.
Step-by-step explanation:
In order to derive a standard sum of products (SOP) expression, we need to create a truth table for each logical argument. The truth table will outline all possible combinations of inputs and their corresponding output values. Based on the truth tables, we can generate a SOP expression by identifying the rows where the output is true (1) and creating a product term for each row. For example, if there are three input variables A, B, and C, and the output is true (1) when A is true (1) and B and C are false (0), then the SOP expression would be (A'BC').
To derive a standard product of sums (POS) expression, we need to create a truth table as well. However, this time we look for the rows where the output is false (0). From these rows, we create a sum term for each row. For example, if the output is false when A is false (0) and B and C are true (1), then the POS expression would be (A+B'+C').