A major advantage of two's-complement representation which hasn't yet been mentioned here is that the lower bits of a two's-complement sum, difference, or product are dependent only upon the corresponding bits of the operands. The reason that the 8 bit signed value for -1 is 11111111 is that subtracting any integer whose lowest 8 bits are 00000001 from any other integer whose lowest 8 bits are 0000000 will yield an integer whose lowest 8 bits are 11111111. Mathematically, the value -1 would be an infinite string of 1's, but all values within the range of a particular integer type will either be all 1's or all 0's past a certain point, so it's convenient for computers to "sign-extend" the most significant bit of a number as though it represented an infinite number of 1's or 0's.

Two's-complement is just about the only signed-number representation that works well when dealing with types larger than a binary machine's natural word size, since when performing addition or subtraction, code can fetch the lowest chunk of each operand, compute the lowest chunk of the result, and store that, then load the next chunk of each operand, compute the next chunk of the result, and store that, etc. Thus, even a processor which requires all additions and subtractions to go through a single 8-bit register can handle 32-bit signed numbers reasonably efficiently (slower than with a 32-bit register, of course, but still workable).

当使用C标准所允许的任何其他有符号表示时，结果的每一位都可能受到操作数的任何位的影响，这就需要将整个值一次保存在寄存器中，或者在计算之后进行额外的步骤，至少在某些情况下，需要读取、修改和重写结果的每个块。

使用2的补码是因为它更容易在电路中实现，也不允许负零。

如果有x位，2的补码范围从+(2^x/2+1)到-(2^x/2)。补码将从+(2^x/2)到-(2^x/2)，但允许负数为零(0000在4位1的补码系统中等于1000)。

维基百科说明了一切:

二补系统的优点是不需要加减电路检查操作数的符号来决定是加还是减。这一特性使系统实现更简单，能够轻松地处理更高精度的算术。此外，零只有一种表示，避免了与负零相关的微妙之处，这种微妙之处存在于补体系统中。

换句话说，无论数字是否为负，加法都是一样的。

这是为了简化数字的和和和差。2的补数中一个负数和一个正数的和与正常方式的和是一样的。

It's worthwhile to note that on some early adding machines, before the days of digital computers, subtraction would be performed by having the operator enter values using a different colored set of legends on each key (so each key would enter nine minus the number to be subtracted), and press a special button would would assume a carry into a calculation. Thus, on a six-digit machine, to subtract 1234 from a value, the operator would hit keys that would normally indicate "998,765" and hit a button to add that value plus one to the calculation in progress. Two's complement arithmetic is simply the binary equivalent of that earlier "ten's-complement" arithmetic.

2的补数允许以正常的方式进行加减法(就像对无符号数字进行绕线运算一样)。它还防止了-0(一种单独的表示0的方法，如果使用常规的逐位比较数字的方法，它将不等于0)。