为什么偏向负数？

Question

If on my compiler, int is of 16 bits, then it's range is -32768 to 32767(in a 2's complement machine).
I want to know why negative numbers have 1 extra no. ie positive numbers go to 32767 but negative go to one more ie-32768.

How -32768 is represented on a 2's complement m/c?

Answer 1

On 16 bits you can fit pow(2,16) (2 to the power of sixteenth) different combinations to represent 65536 numbers. It was decided that zero looks best represented natively as 000...000 and positive numbers in "two's complement" system are normally readable (they're equal to so called "natural binary" representation like 0000 0000 0000 0101 = 5 decimal etc).

Negative numbers in two's complement start with 1111 1111 1111 1111 to represent -1. Think about it as a counter dial with numbers that goes 997, 998, 999 and suddenly when it has to represent 1000 it overflows and shows 000. The principle is the same here, but the direction is other way around - from ...000 to ...111. -2 is represented as 1111....1110 and so on.

Lowest possible number in two's complement will have 1 on front and zeroes on the rest of digits.

Answer 2

If you're looking for a simple, down to earth answer:

There isn't any bias. There are equal amount of numbers on positive and negative side, positive numbers just start from 0 and negative from -1, so hence the difference of one. :)

Answer 3

There isn't really any 'biasing'. The number is negative when the most significant bit is set. For "positive number space" (ie, MSB is not set), as well as 1-32767, you have zero, hence the apparent lack of 32768.

-32768 would be represented by 0b1000000000000000. See link text

Answer 4

There is no negative zero. (-0). Thats why it appears to be a bias. Really it is considered negative if the last bit is set. There is still another 7bits in a byte that can be set in both the positive and negative range.

Answer 5

Another way to think of it is making a 1 bit signed variable. Signed means there must be negative numbers and of course there will be positive numbers. So you can have 1 positive one negative, what two numbers do you pic? now lets make it 2 bits, what 2 positive and negative do you pic? really the secret is the last bit represents negative.

Theres extra work if we want to consider 0 a negative number. and it would be wasteful to have a negative 0.