什么是 1 的补码加法？

Question

https://www.ietf.org/rfc/rfc1071.txt

I see "1's complement addition" is mentioned above. But I don't find its official definition. Could anybody let me know what it is defined?

Answer 1

In ones' complement arithmetic, the last carry bit is wrapped around and added to the result ( end-around carry ). This is also described in RFC 1071 :

On a 2's complement machine, the 1's complement sum must be computed by means of an "end around carry", ie, any overflows from the most significant bits are added into the least significant bits.

In pseudocode, this could be implemented like this:

Function Sum(a: Int16, b: Int16): Int16 {
    c: Int32 := a + b
    return (c AND 0xFFFF) + (c >> 16)
}

Example

   F000
 + 1009
-------
   0009
 + 0001 // add carry
-------
   000A

The reason the ones' complement arithmetic is used in RFC 1071 is, I guess, that many computer systems used it at the time the Internet Checksum was developed in the 1970s. This Wikipedia page describes why the end-around carry is necessary when the bits represent signed integers.

Answer 2

1's complement is a number representation where to take the negative of a number, you simply flip all the bits. Addition in this format would simply involve representing numbers as such, then performing binary addition.