In the video it is told that when we use signed int that is the default case, first bit is reserved for sign convention, 1 for negative and zero for positive… so If we want to write 5 it is 000000000…101, where we can say that the first 0 is for positive sign and following zeros and ones are for 5 and if we want to write -5 it should be simply, 10000…101, where the first 1 is for negative sign and the following zeros and one represent 5. But here comes the 2’s compliment form, which shows that what i just told is wrong. so i am confused… please help me out in this.
one more doubt:-
signed short int range is -2^15 to 2^15 -1
but why is it so?
it should be from -(2^15-1) to 2^15 - 1 as if it is signed we have 15 bits left out of 16…and maximum no. which can be stored in these bits is (2^15 -1) and we can put the sign in the first bit… so it should be -(2^15-1) to 2^15 - 1… please explain…
CPP-Datatype and storage video doubt
Hello @Sheenagoyal21,
This is because of the way numbers are stored in memory.
Signed numbers are stored using something called “two’s complement notation”.
Remember all variables have a certain amount of bits. If the most significant one of them (the one on the left), is a 0, then the number is non-negative (i.e., positive or zero), and the rest of the bits simply represent the value.
However, if the leftmost bit is a 1, then the number is negative.
The real value of the number can be obtained by subtracting 2^n from the whole number represented (as an unsigned quantity, including the leftmost 1), where n is the amount of bits the variable has(it is compiler dependent).
In your case, for signed short int, n=16
Since only n - 1 bits are left for the actual value (the “mantissa”) of the number, the possible combinations are 2^(n - 1). For positive/zero numbers, this is easy: they go from 0, to 2^(n - 1) - 1. That -1 is to account for zero itself – for instance, if you only had four possible combinations, those combinations would represent 0, 1, 2, and 3 (notice how there’s four numbers): it goes from 0 to 4 - 1.
For negative numbers, remember the leftmost bit is 1, so the whole number represented goes between 2^(n - 1) and (2^n) - 1 (parentheses are very important there!). However, as I said, you have to take 2^n away to get the real value of the number. 2^(n - 1) - 2^n is -(2^(n - 1)), and ((2^n) - 1) - 2^n is -1. Therefore, the negative numbers’ range is -(2^(n - 1)) to -1.
Put all that together and you get -2^(n - 1) to 2^(n - 1) - 1. As you can see, the upper bound gets a -1 that the lower bound doesn’t.
And that’s why there’s one more negative number than positive.
Hope, it would help.
Give a like, if you are satisfied.