-5 in computer VS in actual. 2's complement

#1

5 = 00000101

-5 = ~5 + 1
= 11111010 + 1 = 11111011

But, 11111011 is not 5 in decimal. So what is -5 in binary ?

#2

Hi @anuj_it you have correctly formulated -5 in binary i.e. 11111011 , i think you are confused in how computer percives negetive number

lets think like how a compter thinks when it recieves 00000101 and 11111011 (consider int as 8 bit number )

  1. when the computer gets 00000101 it checks its MSB( most significant bit i.e the leftmost bit) since the MSB tells the sign of number (0 for positive and 1 for negetive) thus the computer knows 00000101 is a positive number so it will calculate it as usual and we get 5 in decimal
    but things are interesting for negetive number
  2. when the computer gets 11111011 it check it MSB , which is 1 this means this number is a negetive number ,as the computer knows that the number is in 2’s compliment . thus it takes its 2’s compliment i.e 00000100+1 which is 00000101 which is 5 and puts a -ve sign with it . thus we get -5 as the result

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#3

Ok… so 10000001 (binary form) would be a -ve number and not 129 ?

#4

And if someone asks me what is binary of -5, so ans would be 11111011 ?
And if its written somewhere 11111011, so how will I come to know whether its -5 or 251 ?

#5

by its most significant bit if 1 then its a negetive number and 0 then positive if we are dealing with 8 digit binary numbers than 11111011 then its -5 and if we are dealing with 32 bit number then it is 251

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#8

The most common encoding of negative numbers in processors is not using 1’s complement but 2’s complement.

Using 2’s complement 00000101 is 5, but 11111010 means -6, not -5.

If we use the common addition rule we get 11111111 which is -1 as expected.

We can see it another way: if we were using 1’s complement for encoding negative numbers then what would be the opposite of zero (encoded as 00000000) ? Wouldn’t it be 11111111 ?
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