4-bit parallel adder — adding 1011 and 1111 with Cin = 1 Two 4-bit binary numbers (A = 1011 and B = 1111) are applied to a 4-bit parallel adder with carry-in Cin = 1. What are the resulting 4-bit sum (∑4∑3∑2∑1) and the carry-out (Cout)?

Introduction / Context:
Parallel adders compute multi-bit sums in one stage by chaining full-adders. Understanding how carries propagate and how the final carry-out relates to overflow or extended precision is essential for designing arithmetic units.

Given Data / Assumptions:

• A = 1011 (decimal 11), B = 1111 (decimal 15).
• Cin = 1.
• Unsigned addition with a 4-bit adder.

Concept / Approach:
Add the operands plus Cin arithmetically, then separate the lower 4 bits as the sum and the 5th bit as Cout. This mirrors the ripple-carry adder behavior where carries ripple from LSB to MSB, producing a final carry-out if the total exceeds 15.

Step-by-Step Solution:

Verification / Alternative check:
Perform bitwise addition: start from LSB, track carries, and verify final sum 11011, which splits into Cout=1 and 4-bit sum 1011.

Why Other Options Are Wrong:

• 0111, 1111, 1100 with Cout shown: none match the correct 5-bit result of 11011.

Common Pitfalls:
Losing the final carry-out or misaligning bit positions when reading the 5-bit total back into 4-bit sum plus Cout.

Final Answer:
∑4∑3∑2∑1 = 1011, Cout = 1