Negating an (unsuffixed) integer constant: The expression -(-2147483648) is perfectly defined in C, however it may be not obvious why it is this way. When you write -2147483648, it is formed as unary minus operator applied to integer constant. If 2147483648 can’t be expressed as int, then it s is represented as long or long … Read more
2147483647 + 1 is evaluated as the sum of two ints and therefore overflows. 2147483648 is too big to fit in an int and is therefore assumed by the compiler to be a long (or a long long in MSVC). It therefore does not overflow. To perform the summation as a long long use the … Read more
Two’s complement subtracts off (1<<bits) if the highest bit is 1. Taking 8 bits for example, this gives a range of 127 to -128. A function for two’s complement of an int… def twos_comp(val, bits): “””compute the 2’s complement of int value val””” if (val & (1 << (bits – 1))) != 0: # if … Read more
Assume for the sake of contradiction that there exists some x and some y (mod 2n) such that ~(x+y) == ~x + ~y By two’s complement*, we know that, -x == ~x + 1 <==> -1 == ~x + x Noting this result, we have, ~(x+y) == ~x + ~y <==> ~(x+y) + (x+y) == … Read more
It’s done so that addition doesn’t need to have any special logic for dealing with negative numbers. Check out the article on Wikipedia. Say you have two numbers, 2 and -1. In your “intuitive” way of representing numbers, they would be 0010 and 1001, respectively (I’m sticking to 4 bits for size). In the two’s … Read more
Two’s complement is a clever way of storing integers so that common math problems are very simple to implement. To understand, you have to think of the numbers in binary. It basically says, for zero, use all 0’s. for positive integers, start counting up, with a maximum of 2(number of bits – 1)-1. for negative … Read more