Why is the difference in +ve & -ve Vlaues? Very BASIC question!

Question

Can anyone tell me why there is a differene in -ve and +ve values of integers/floats etc?
I mean to say that as in C++, an character's max ve value is 127. While its -ve value is -128.
I need 2's complement procedure remembering that in 8-bit pattern in RAM, most significant bit is sign bit.
Please, answer with exapmles. (Same is true for java)

Answer 1

hasan_asd,
Lets take 8 bits for example. With 8 bits there are 256 different combinations, correct. 2 ^ 8 = 256. To a computer, this is just a collection of 8 ones or zeros. We as humans want it to represent a number. We can up with two different ways to approach it. The first way is to have the 8 bits represent an unsigned number. That is, all the numbers are positive. so that possible values that could exist for 256 combinations would be 0 to 255. The second way is for us to say, oh but our we want a negative number as well. So, we made up the rule that the far left bit would represent a negative sign. We then called this a signed number. For a signed number to be positive, the far left bit will be 0. So, the highest positive number we can have is 01111111 and that equals 127. Now, if we change the far left bit to a 1. The remaining seven bits are the value in the negative direction. So, 11111111 = -127 for a signed number. That leaves one combination left for signed numbers and that is 10000000. What number is this suppose to be. Keep in mind that the far left bit represents negativity for signed numbers, so It can't be +128. Also, keep in mind that we have only used up 255 possible combinations of our 256, so, since it is a negative number, it must be -128. I hope this helped. Just remember that the eight-bit pattern you have depends on what the programming language considers it to be. With C++ you can physically declare it as signed or unsigned, but in Java it is unsigned.
tajenkins