17. Implementing Logic Circuits from Expressions

Once a Boolean expression is minimized (either SOP or POS), the next step is to translate it into a physical circuit using logic gates.

SOP Implementation (AND-OR Structure)

SOP (Sum-of-Products) expressions naturally map to a two-level circuit structure:

1. Level 1: AND Gates: Each product term (e.g., $A\overline{B}C$) requires an AND gate. The inputs to these gates may require inverters if the variable is complemented.
2. Level 2: OR Gate: All the outputs of the AND gates are fed into a single large OR gate to produce the final sum.

Example: $Y = A\overline{B} + B C$

• One 2-input AND gate for $A\overline{B}$.
• One 2-input AND gate for $B C$.
• One 2-input OR gate connects the results.

POS Implementation (OR-AND Structure)

POS (Product-of-Sums) expressions map to the dual structure:

1. Level 1: OR Gates: Each sum term (e.g., $A + \overline{B}$) requires an OR gate.
2. Level 2: AND Gate: All the outputs of the OR gates are fed into a single large AND gate to produce the final product.

Using Universal Gates (NAND/NOR)

In many applications, ICs only contain NAND or NOR gates. We can implement any SOP circuit using only NAND gates (NAND-NAND configuration) and any POS circuit using only NOR gates (NOR-NOR configuration). This is achieved by applying De Morgan's theorems to push the inversions through the gates.