Are "the AND-OR forms of combinations" and "sum-of-products" exactly the same?

Are "the OR-AND forms of combinations" and "product-of-sums" exactly the same?

In "the AND-OR and OR-AND forms of combinations", is single NOT gate applied only to literals?

In "sum-of-products and product-of-sums", is single NOT gate applied only to literals?


The terminology comes from Mano's Digital Design:

The sum-of-products and product-of-sums are mentioned in Section 2.6 Canonical and Standard Forms in Chapter 2 Boolean Algebra and Logic Gates,

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and are simplified in Section 3.2 The Karnaugh Map Method and in Section 3.4 Product-of-Sums Simplification.

The AND-OR and OR-AND forms of combinations are mentioned in Section 3.7 Other Two-Level Implementations in Chapter 3 Gate-Level Minimization.

The types of gates most often found in integrated circuits are NAND and NOR gates. For this reason, NAND and NOR logic implementations are the most important from a practical point of view. Some (but not all) NAND or NOR gates allow the possibility of a wire connection between the outputs of two gates to provide a specific logic func- tion. This type of logic is called wired logic.


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  • \$\begingroup\$ Invert terms. Change operators. And they are the same. \$\endgroup\$ Sep 21, 2020 at 15:18

1 Answer 1


Sum of products and product of sums are two ways to write the expression for a combinatorial logic function using symbols, as in the example, "\$F_1 = y' + xy + x'yz'\$".

AND-OR and OR-AND are two ways to connect physical gates to implement a logical function.

There is a close relationship between them, but one is about expressing logic with symbols and the other is about building actual circuits to implement the logic.


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