twos-complement

I still haven't found a reason why the lowest signed negative number doesn't have an equivalent signed positive number? I mean in a 3 digit binary number for simplicity 100 is -4? but we can't have a positive 4 in signed format because we can't. It overflows. So how do we know two's complement 1000 is -4 1000 0000 is -128 and so on? We have no original positive number 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

I'm designing a simple toy instruction set and accompanying emulator, and I'm trying to figure out what instructions to support. In the way of arithmetic, I currently have unsigned add, subtract, multiply, and divide. However, I can't seem to find a definitive answer to the following question: Which of the arithmetic operators need signed versions, and for which are the unsigned and two's complement signed versions equivalent? So, for example, 1111 in two's complement is equal to -1. If you add 1 to it and pretend that it's an unsigned number , you get 0000, which is correct even when thinking

I thought the whole point of 2's complement was that operations could be implemented the same way for signed and unsigned numbers. Wikipedia even specifically lists multiply as one of the operations that benefits . So why does x86 have separate instructions for each, mul and imul ? Is this still true for x86-64? Addition and subtraction are the same, as is the low-half of a multiply. A full multiply, however, is not. Simple example: In 32-bit twos-complement, -1 has the same representation as the unsigned quantity 2**32 - 1. However: -1 * -1 = +1 (2**32 - 1) * (2**32 - 1) = (2**64 - 2**33 + 1)

How does C represent negative integers? Is it by two's complement representation or by using the MSB (most significant bit)? -1 in hexadecimal is ffffffff . So please clarify this for me. 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 representations, positive

I was using -1 as a flag value for a function whose return type is size_t (an unsigned type). I didn't notice it at first, particularly because it wasn't causing any errors in my code (I was checking it with x == -1, not x < 0). Are there any subtle reasons I shouldn't leave it as is? When might this behave unexpectedly? Is this commonly used? ptrdiff_t is less common, takes longer to type, and anyway it's not really the appropriate type since the function returns an index into an array. -1 will always convert to the max unsigned value, this is due to section 4.7 Integral conversions : If the

Is there a built in function in python which will convert a binary string, for example '111111111111', to the two's complement integer -1? travc 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 sign bit is set e.g., 8bit: 128-255 val = val - (1 << bits) # compute negative value return val # return positive value as is Going from a binary string is