Boolean Standard Form

Abstract

---

• When it is expressed in Sum-of-Products (SOP) or Product-of-Sums (POS)

Important

Every Boolean expression can be expressed in either SOP (Sum of Products) or POS (Product of Sums) form. We can convert from one form to the other by taking the complement of the current form.

Test your understanding!

X' + Y + Z is SOP, it is also POS because X' + Y + Z as a whole is Sum Term.

X · (W' + Y · Z) isn’t SOP, because it isn’t a Boolean Literal, and of multiple boolean literals, or of multiple product terms. It isn’t POS too, because it isn’t or of multiple boolean literals, and of multiple sum terms.

X·Y·Z' is POS, because the whole is Product Term, it is also SOP

Boolean Variable

• A variables that hold either true or false

Boolean Literal

• A Boolean Variable on its own or its complemented form

Product Term

---

• A single Boolean Literal or a single AND of several Boolean Literals

Sum-of-Products (SOP)

• A Product Term or a OR of multiple Product Term
• Used in Minterm

Sum Term

---

• A single Boolean Literal or a single OR of multiple Boolean Literals

Product-of-Sums (POS)

• A single Sum Term or AND of multiple Sum Term
• Used in Maxterm