二进制表示 - 7 位二进制补码

Question

我们可以用 7 位二进制补码表示的最大负数是多少？

Answer 1

With 7-bits of 2's complement, it could range from -64 to 63. (traditionally, 7 bits can only go up to 2^n-1 which is 128 but MSB is reserved for sign, so we could have 6 bits to represent the data. We will be getting 64 positive and 63 negative values and answer should be -64, 63.)

No, because in two's complement, the most significant bit is the sign bit. 0000001 is +1, a positive number.

That is why the range of two's complement 7-bit numbers is -64 to 63, because 64 is not representable (it would be negative number otherwise).

The most negative number is 1000000. The leading 1 tells you it's negative, and to get the magnitude of the number, you flip all the bits (0111111), then add one (1000000 = 64). So the resulting number is -64 thru 63.