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two's complement aritmetic

 
Arno Du Toit
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Please can someone give me a clear and simple explanation on how to convert a positive binary number to a negative one. I have come alot of explanations where they say you have to invert the bits and then add one. I have tried to do this, but they do not eplain where you have to add the one. Please explain or point me to an explanation.
Here is an example. 5 in binary is 0101. Invert the bytes you get 1010 then if you add one and drop th e0 at the end you get 1011 which apparently is -5. If you take another number like which is 0110 and you invert it you get 1001, now where do you add the one?? I know the answer is 1010. And then my final question how would you convert a negative binary to a positive one?
 
zarina mohammad
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i found this explanation in one of the threads here ...
Proceed as follows to get the decimal equivalent of a -ve number:
say -8
1. Invert all the bits.
--> so 1111 1000 becomes 0000 0111.
2. Strip all the leading zeros and convert to decimal.
--> so 0000 0111 becomes 111 which is equivalent to 7.
3. Add 1 to the result and then put the negative sign.
--> 7+1 = 8 and finally it becomes -8.
so 1111 1000 = -8.
To convert a -ve decimal to a binary just do the reverse.
Taking the example of -8
1.Strip it off the -ve sign and subtract 1.
-->so -8 becomes 8 and then 7.
2. Convert the decimal to binary
-->7 is 0000 0111 in binary.
3.Invert the bits
-->Result is 1111 1000. (same as the start of this message)

hope this helps
zarina
 
Dave Vick
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Anthony Villanueva
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You can also try the Javaranch tutorial on bit manipulation.
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Valentin Crettaz
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Here are some lessons on 2's complement arithmetic:
http://www.javaforstudents.co.uk/bitty.html
http://www.javaforstudents.co.uk/secondbit.html
 
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