Understanding 2's Complement w/ 4 Bits

[ECE]

Why in 2's complement the range of numbers that can be represented with 4 bits are from -8 to +7? Wouldn't the numbers with 4 bits be till 15? I am confused.Please help me out.

-Thankyou

 

[Corneo]

Read this, I think this article explains it well.

http://en.wikipedia.org/wiki/2's_complement

 

[chroot]

With four bits, you can store 16 different values. You make them represent 0 through 15, which is called unsigned magnitude, or you can make them represent -8 through +7, which is called 2's complement. You cannot represent all the numbers from, say, -8 to +15, because you do not have enough bits.

- Warren