[SOLVED] How to add 3 or more two's complement binary numbers

[panda1234]

Hi,
We know if we want to add to number in two's complement we can do first sign extension and then add to number in this way if we have a carry in last we ignore carry.
But in 3 or 4 number we may have carry more than 1 in this way what do we do with carry?
(Please explain me with example)
thanks

 

[betwixt]

Exactly the same, just take the total of numbers 1 and 2, add the total with the carry to number 3 then using that as the new total add it and the carry to number 4. Do it progressively rather than trying to handle several carry bits at once.

Brian.

 

[panda1234]

Thanks but can you take an example? for example add 1111+1001+1111

 

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here is an example of adding up some positive and negative numbers:

[FONT=Courier New]14
-9 = +5
+8 = +13
-12 = +1
-10 = -9

binary => 2's comp
 01110 => 01110
-01001 => 10111
 01000 => 01000
-01100 => 10100
-01010 => 10110

Adding them up
 01110
+10111
=00101 +5 (note there is a carry of 1 here, which is thrown away)
+01000
=01101 +13
+10100
=00001 +1
+10110
=10111 -9[/FONT]

- - - Updated - - -

Thanks but can you take an example? for example add 1111+1001+1111

That is -9 which can't be represented in 4-bits if we sign extend:

 11111
+11001
=11000
+11111
=10111

 

[panda1234]

Thanks but you adding them two by two i want to adding them all in one step.
if our numbers not in two's complement we can do this shown below:
https://courses.cs.vt.edu/csonline/NumberSystems/Lessons/AddingMultipleBinaryNumbers/index.html

 

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I had a feeling you were going to make some comment about doing it in one step. As I'm a hardware type, I was thinking (hoping) you weren't just asking about the math, but wanted to know how to implement the math in hardware.

Thanks but you adding them two by two i want to adding them all in one step.

You could do that but that makes for an unnecessarily complex design. If this is just a binary 2's complement math exercise then:

c4  1                  carry from 4th column
c3  1   0              carry from 3rd column
c2      1   0          carry from 2nd column
c1          1   0      carry from first column
    1   1   1   1   1  -1
  + 1   1   0   0   1  -7
  + 1   1   1   1   1  -1
  + 1   1   1   1   1  -1
  + 0   1   1   1   1  +15
  110 110 101 100 101  number of 1's in the column
  = 0   0   1   0   1
= +5

to ensure the calculation doesn't over/under flow you should probably sign extend by half the number of adds (e.g. in this case sign extend by 2 bits, 4 adds, before hand to ensure you'll never over/under flow)