I was facing a problem in converting not of a number i.e. ~X. Though I know the method ... 1. find the binary of the number and 2. revese all the bits. It can be done but is a SLOW process when you are short of time in exam. for eg. what is ~4569? It will take time. find binary of 4569 will take time manually in exam. I found a VERY FAST method somewhere on net. fast method ~x = -x -1 i.e. ~4569 = -4569 -1 = -4570. or ~-1234 = --1234 -1 = 1233. simple isnt it? I thought this might be usefule to many in exam and hence posted on saloon. Suggestions welcome.
The reasoning behind this formula is as follows: 1) Complement of a number is basically inverting the bits i.e. 0 ->1 and vice versa. So, when we put a '-' sign in front of a no, then internally, this is calculated in 2s complement form:- first invert the bits (i.e. 1's complement) and then add 1 to this complemented number. 2) Since, we are just intrested in the inverted bits, subtracting 1 from the above inverted number will st away give the 1s complement form of the original no. In short, for -2: 2 -> 0010 -2 -> in 2s complement is: 1's complement + 1 i.e 1s complement of 2 = ivert bits of 0010 = 1101 now adding 1 gives: 1110 which is the 2s complement form of -2 Hence, doing exactly the opposite of last step would give as the desired quick answer for getting ~2.