title: Adding 8 bit numbers using signed 2's complement
body: <p>Either there is some confusion with what is written below or my textbook is wrong.
  I was looking at examples in my textbook for addition of 8 bit signed binary digits using 2's complement and came across these examples.
  We are required to find if any overflow occurs</p>
  
  <hr>
  
  <p>Example 1]</p>
  
  <p>Adding +75 and -58</p>
  
  <p>+75 = 01001011 ... (a)<br>
  +58 = 00111010<br>
  -58 = 11000110 ... (b) [took 2's complement of +58] <br></p>
  
  <p>now adding (a) and (b) we get</p>
  
  <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;01001011<br>
  + &nbsp;&nbsp;11000110<br>
  &nbsp;&nbsp;1]00010001</p>
  
  <p>It was written in textbook that overflow occurs with an arrow pointing to that extra 1 separated with a square bracket.
  This example is ok and from here I understood that if there is and extra 1 then we have a overflow.</p>
  
  <p>(Question 1: Am i correct with what i understood ?)</p>
  
  <hr>
  
  <p>Example 2: This example confused me</p>
  
  <p>Add 53 and (-13)</p>
  
  <p>53 =    00110101<br>
  -(13) = 11110011</p>
  
  <p>now adding both we get</p>
  
  <p>00110101 + 11110011 = 1]00101000</p>
  
  <p>And then they wrote: Carry in and carry out for signed bit is 1. So no overflow. Discarding the carry bit and rest is the positive required result</p>
  
  <p>(The main Question: Even though there was this overflow digit(extra 1) why did they say its not overflow. And what are these carry in and carry out for signed bit written in above sentence.)</p>
  
  <hr>
  
  <p>I did a lot of Google search but couldn't find a good reasonable solution to this line they talked about, or may be it was in front of my eyes but i didn't understand. Somebody please clarify. Most examples I saw(on stack-overflow and other sites) were for 4 bits that confused a bit more. Somebody please help me clarify, Thanks.</p>