Sum Of Product (SOP) Form

Q.1: What is difference between Canonical and Non-canonical form?

Answer:

This are two different ways to represent boolean expressions in Sum of Product (SOP) form. In canonical form , every product term contains all variables of the function and are included in either true or complementary form. On the other hand, in non-canonical form, product terms may or may not include all variables, and they may also can include all variables. For systematic representation canonical SOP form is used , while ono-canonical form is more concise.

Q.2: How to write Boolean expression in SOP form from truth table?

Answer:

• Take the rows with output 1 in given truth table.
• From the selected rows, convert the inputs in their true or complementary form.
• Write product terms for each product term. Use logical AND in between input variables.
• Combine all product terms using logical OR operation.

Q.3: How can I simplify a Boolean expression in the Sum of Products (SOP) form?

Answer:

We can use boolean algebra rules and law to simplify the equation

1. A + AB = A (Absorption Law)
2. A’BC + AB’C + ABC = A’BC + AB’C (Consensus Theorem )
3. AB + AC = A(B + C) (Distribution)
4. (A + B)’ = A’B’ (Demorgans Theorem)
5. Eliminate repeated terms , and the terms that have no impact on the function.
6. A + A’ = 1, AA’ = 0 (complement law)

In Digital Electronics any logic circuit’s output is the function of digital inputs and the relation between input and output can be represented using logic table or boolean expressions.

This Boolean expression can be represented in two forms.

1. Sum of Product (SOP)
2. Product of Sum (POS)