Two's compliment of SIGNED binary

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Discussion Overview

The discussion revolves around the concept of two's complement representation for signed binary numbers, exploring how it differs from regular binary numbers and addressing potential confusion regarding different representations such as sign-magnitude and one’s complement.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant describes the process of finding the two's complement for regular binary numbers and seeks clarification on how to apply it to signed numbers.
  • Another participant explains that signed numbers in two's complement are treated similarly to regular binary, providing an example with the number 1 and its two's complement representation.
  • A participant expresses confusion over differing answers provided by their lecturer and questions whether the two's complement is the only method for calculating signed binary numbers.
  • Some participants mention alternative representations, such as sign-magnitude and one’s complement, noting that these are not considered regular binary numbers in the context of two's complement.
  • There is a suggestion that the lecturer may have referenced a different question, leading to the confusion regarding the answers provided.

Areas of Agreement / Disagreement

Participants generally agree on the method of calculating two's complement for signed numbers, but there is uncertainty regarding the lecturer's approach and the potential for different representations, indicating that multiple views remain on the topic.

Contextual Notes

Participants mention different binary representations, but the discussion does not resolve the implications of these alternatives on the understanding of two's complement.

fractal01
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The twos compliment for regular binary numbers- you just replace all 1's by 0's and 0's by 1's and then +1. So how would you go about finding out for signed...I have got as far as changing the first digit then that's it! Does anyone know what to do?
 
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Hi fractal01! :smile:

"Signed" is the same thing (at least in 2's complement, which is pretty standard).

Suppose you take the number 1.
The binary representation is: 0001
The 2's complement is 1110+1=1111.
This is the same as the representation for -1.

Suppose you add them:
0001 + 1111 = (1)0000.

Yes! It is zero! (disregarding the carry over)
 
I like Serena said:
Hi fractal01! :smile:

"Signed" is the same thing (at least in 2's complement, which is pretty standard).Yes! It is zero! (disregarding the carry over)

Hey! Thank you so much! My lecturer gave us some questions and in one of the answers he came up with something completely different and it was the only example so I have been struggling over it for at least half an hour! Everyone is human I guess and makes mistakes...but are you sure that this is the only way of calculating this?
 
fractal01 said:
...but are you sure that this is the only way of calculating this?

This is the way the 2's complement representation and its associated "signed" works.

There are other representations, such as 1's complement (unusual), and a representation with a separate sign bit (used for floating point), but those are not "regular" binary numbers.

So what did your lecturer come up with?
 
It could be sign-magnitude representation.
 
aralbrec said:
It could be sign-magnitude representation.

That's what I said or what I at least intended:
"a representation with a separate sign bit (used for floating point)"
 
I like Serena said:
That's what I said or what I at least intended:
"a representation with a separate sign bit (used for floating point)"

Thanks for all of your help! You are right. He just looked at a different question when he was writing the problem I think.
 
aralbrec said:
It could be sign-magnitude representation.
Thanks
 

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