Digital logic design – parity generation using adders Could the SUM output (S) of a full-adder be used to generate the parity bit for two data inputs?

Introduction / Context:
Parity generators are common in digital systems for simple error detection. A full-adder’s SUM output implements exclusive-OR behavior among its three inputs. This question explores whether the SUM output can directly act as a parity generator for two bits.

Given Data / Assumptions:

• Full-adder inputs: A, B, and Cin.
• Full-adder SUM output S = A XOR B XOR Cin.
• Two-bit parity requires S = A XOR B when Cin = 0 for odd parity.

Concept / Approach:
The parity bit for two data inputs is the XOR of those inputs. Because a full-adder SUM equals XOR of all three inputs, tying Cin to 0 makes S = A XOR B. That is exactly an odd-parity result for two bits. If even parity is required, Cin can be tied HIGH to invert the parity.

Step-by-Step Solution:
Define parity: For two bits, odd parity = A XOR B.Use full-adder: S = A XOR B XOR Cin.Tie Cin = 0: S = A XOR B → odd parity bit for two inputs.Tie Cin = 1: S = NOT(A XOR B) → even parity bit for two inputs.

Verification / Alternative check:
Truth-table check for A,B in {00,01,10,11} confirms S toggles exactly as a 2-bit parity output when Cin is fixed.

Why Other Options Are Wrong:
No / conditional answers: They overlook that selecting Cin = 0 or Cin = 1 sets odd or even parity respectively.

Common Pitfalls:
Confusing SUM with addition; remember that SUM is bitwise XOR with Cin, not a majority function.

Final Answer:
Yes