Your program is invoking undefined behavior because of an overflow in the conversion from floating-point to integer. What you see is only the usual symptom on x86 processors. The float value nearest to 2147483584 is 231 exactly (the conversion from integer to floating-point usually rounds to the nearest, which can be up, and is up … Read more
You are actually quite close. In binary , not 0 should be 1 Yes, this is absolutely correct when we’re talking about one bit. HOWEVER, an int whose value is 0 is actually 32 bits of all zeroes! ~ inverts all 32 zeroes to 32 ones. System.out.println(Integer.toBinaryString(~0)); // prints “11111111111111111111111111111111” This is the two’s complement … Read more
The width used in format is always a minimum width. In this case, instead of using sub string operations I would suggest: String.format(“%05X”, decInt & 0xFFFFF);
Oddly, the reason this works with -1 is exactly the same as the reason that this works with zeros: in two’s complement binary representation, -1 has 1s in all its bits, regardless of the size of the integer, so filling in a region with bytes filled with all 1s produces a region of -1 signed … Read more
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
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
Let’s start by summarizing Java primitive data types: byte: Byte data type is an 8-bit signed two’s complement integer. Short: Short data type is a 16-bit signed two’s complement integer. int: Int data type is a 32-bit signed two’s complement integer. long: Long data type is a 64-bit signed two’s complement integer. float: Float data … 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