SOP vs POS in Boolean Algebra

What is SOP (Sum of Products)?

• SOP is a series of AND terms added together (ORed).

• Each product term represents a unique combination where the output is 1.

• Example:
  $F(A, B, C) = A \cdot B' \cdot C + A' \cdot B \cdot C$

Used in: Combinational logic, digital gates, circuit simplification.

What is POS (Product of Sums)?

• POS is a series of OR terms multiplied together (ANDed).

• Each sum term represents a condition where the output is 0.

• Example:
  F(A,B,C)=(A+B+C′)⋅(A′+B+C)

Used in: Logic minimization, designing circuits from false outputs.

 SOP vs POS: Key Differences

Canonical vs Non-Canonical Forms

Canonical forms are ideal for deriving expressions directly from truth tables.

How to Derive SOP and POS from a Truth Table

Example Truth Table:

SOP (Use F = 1 rows):

• Row 2: A=0, B=1 → A'·B

• Row 3: A=1, B=0 → A·B'

SOP = A'·B + A·B'

POS (Use F = 0 rows):

• Row 1: A=0, B=0 → (A + B)

• Row 4: A=1, B=1 → (A' + B')

POS = (A + B)·(A' + B')

When to Use SOP or POS?

Real-World Applications

• SOP:

  • Used in control logic, ALUs, and programmable logic arrays (PLAs)

  • Great for circuits that focus on activating outputs (e.g., turning a light on)

  • Found everywhere from elevators and traffic lights to CPUs and IoT devices.

• POS:

  • Ideal for error detection, NOR gate-based systems, or where minimizing OFF states is critical

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