Multiple choice

We consider the addition of two $2's$ complement numbers $ b_{n-1}b_{n-2}\dots b_{0}$ and $a_{n-1}a_{n-2}\dots a_{0}$. A binary adder for adding unsigned binary numbers is used to add the two numbers. The sum is denoted by $ c_{n-1}c_{n-2}\dots c_{0}$ and the carry-out by $ c_{out}$. Which one of the following options correctly identifies the overflow condition?

  1. $ c_{out}\left ( \overline{a_{n-1}\oplus b_{n-1}} \right )$
  2. $ a_{n-1}b_{n-1}\overline{c_{n-1}}+\overline{a_{n-1}b_{n-1}}c_{n-1}$
  3. $ c_{out}\oplus c_{n-1}$
  4. $ a_{n-1}\oplus b_{n-1}\oplus c_{n-1}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Binary adder generates C out only if