All numbers can be represented by any number times 10 to some power. We all know this, so let me not delve into this any more. Now, the reason we cannot use this system of numbering in the computer is pretty simple. Yeah, it would make life easier for us. But, as we know, a computer circuit is made out of transistors.
Transistors have two positions- on and off.
The computer uses these positions to represent 0 and 1. Since we do not have any systems with 10 stable positions, and we do have the transistor with 2 stable positions, we thus use the binary system. The binary system uses base 2 instead of base 10 like we are used to. You can see how any number can be represented by a base of 10. To represent integers, which can be positive or negative, computers typically use a sign notation on the binary. 0 is positive and 1 is negative and this number precedes the the rest of the number.