It’s represented in binary (base 2). Read more about number bases. In base 2 you only need 2 different symbols to represent a number. We usually use the symbols 0 and 1. In our usual base we use 10 different symbols to represent all the numbers, 0, 1, 2, … 8, and 9. For comparison, … Read more
Here’s a reference table that might help. This shows an example of every possible combination of the 4 arithmetic flags that can result from the ADD and SUB instructions on x86. ‘h’ ‘ud’ and ‘d’ stand for hex, unsigned decimal and signed decimal representations of each value. For example, the first row for SUB says … Read more
One of the specific questions considered by the committee was what to do about -INT_MIN, and the results of that poll were: addition / subtraction / multiplication and -INT_MIN overflow is currently undefined behavior, it should instead be: 4: wrap 6: wrap or trap 5: intermediate values are mathematical integers 14: status quo (remain undefined … 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
This seems to trick java into converting the number without forcing a positive result: Integer.valueOf(“FFFF”,16).shortValue(); // evaluates to -1 (short) Of course this sort of thing only works for 8, 16, 32, and 64-bit 2’s complement: Short.valueOf(“FF”,16).byteValue(); // -1 (byte) Integer.valueOf(“FFFF”,16).shortValue(); // -1 (short) Long.valueOf(“FFFFFFFF”,16).intValue(); // -1 (int) new BigInteger(“FFFFFFFFFFFFFFFF”,16).longValue(); // -1 (long) Example here.
One way to think about it is that signed, two’s complement format works by assigning each bit a power of two, then flipping the sign of the last power of two. Let’s look at -4, for example, which is represented as 100. This means that the value is -1 x 2^2 + 0 x 2^1 … Read more
Addition, subtraction and multiplication are the same provided: Your inputs and outputs are the same size Your behaviour on overflow is wraparound modulo 2n Division is different. Many instruction sets offer multiplication operations where the output is larger than the input, again these are different for signed and unsigned. Furthermore if you are writing your … Read more
Consider what you get when you add a number to its bitwise complement. The bitwise complement of an n-bit integer x has a 1 everywhere x has a 0, and vice versa. So it’s clear to see: x + ~x = 0b11…11 (n-bit value of all ones) Regardless of the number of bits in x. … Read more
Because the integer overflows. When it overflows, the next value is Integer.MIN_VALUE. Relevant JLS If an integer addition overflows, then the result is the low-order bits of the mathematical sum as represented in some sufficiently large two’s-complement format. If overflow occurs, then the sign of the result is not the same as the sign of … Read more
ISO C (C99 section 6.2.6.2/2 in this case but it carries forward to later iterations of the standard(a)) states that an implementation must choose one of three different representations for integral data types, two’s complement, ones’ complement or sign/magnitude (although it’s incredibly likely that the two’s complement implementations far outweigh the others). In all those … Read more