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# How to derive Binary representation of Negative Numbers

Vineet Sharma
Ranch Hand
Posts: 51
How can arrive at the binary representation of -192?
I understand how this works for positive numbers, but negative numbers are confusing.
Any feedback will be appreciated.
Thanks,
Vineet

Sridevi Shrikanth
Ranch Hand
Posts: 31
Negative numbers are represented as 2's complement.
Let me take a simple no: 41
Its binary rep is : 00101001
Taking 2's complement is as follows:
Negate the bits and add one to the result:
Negating the bits: 11010110
Add 1 : 11010111
so -41 is 11010111
Hope this helps

Vineet Sharma
Ranch Hand
Posts: 51
Sridevi,
Thanks for the example. However, doing the same for -192 does not seem to work.
Can you please let me know what you arrive at as the solution.
Thanks,
Vineet
Originally posted by Sridevi Shrikanth:
Negative numbers are represented as 2's complement.
Let me take a simple no: 41
Its binary rep is : 00101001
Taking 2's complement is as follows:
Negate the bits and add one to the result:
Negating the bits: 11010110
Add 1 : 11010111
so -41 is 11010111
Hope this helps

Art Metzer
Ranch Hand
Posts: 241
Hi, Vineet.
A little rule that I use when I need to represent negative numbers in binary is
~i = -i-1.
That is, the bitwise inversion of "i" is equivalent to negative "i" less one.
In your example, you're looking for the binary representation of -192. Since -192 = -191-1, the following statement is true:
~191 = -192.
So if we can find the binary representation of 191, then invert all its bits, we will have the binary representation of -192.
This computation requires us to know which data type we are working with: since you didn't specify, I'll assume we are working with ints (32 bits).
191 = 2**7 + 2**5 + 2**4 + 2**3 + 2**2 + 2**1 + 2**0
+191 = 00000000 00000000 00000000 10111111
then
~191 = 11111111 11111111 11111111 01000000 = -192.
I hope this helps, Vineet.
Art

Vineet Sharma
Ranch Hand
Posts: 51
Art,
Thanks a lot for your help. Your method makes things very easy.
Thanks again,
Vineet
Originally posted by Art Metzer:
Hi, Vineet.
A little rule that I use when I need to represent negative numbers in binary is
~i = -i-1.
That is, the bitwise inversion of "i" is equivalent to negative "i" less one.
In your example, you're looking for the binary representation of -192. Since -192 = -191-1, the following statement is true:
~191 = -192.
So if we can find the binary representation of 191, then invert all its bits, we will have the binary representation of -192.
This computation requires us to know which data type we are working with: since you didn't specify, I'll assume we are working with ints (32 bits).
191 = 2**7 + 2**5 + 2**4 + 2**3 + 2**2 + 2**1 + 2**0
+191 = 00000000 00000000 00000000 10111111
then
~191 = 11111111 11111111 11111111 01000000 = -192.
I hope this helps, Vineet.
Art