"how numbers are stored in computers"
Humans represents numbers in base 10 - that is, with 10 different digits.
Each digit corresponds to a power of 10. Humans also occassionally write numbers in base 16, where the letters a through f represent the numbers 10 through 15.
Regardless of which human representation you choose, a computer will represent that number in base 2, with only the digits 0 and 1. This roughly corresponds to the presence or non-presence of an electrical current.
Each digit of a binary number is referred to as a bit.
You can experiment with the 8 bit binary number below, by clicking on the bits to change them from 0 to 1.
=0
Each digit represents a power of 2, just like our human numbering system uses each digit to represent a power of 10. A group of 8 bits is called a byte, and a single byte can represent 28 (256) different values.
=0
In the example above, we are using 8 bits to represent an unsigned integer. If we want to store negative numbers, we can dedicate 1 bit as a sign bit to store 0 for positive numbers and 1 for negative numbers.
sign=0
Try clicking the sign bit to see how the resulting value changes. If we allowed the sign bit to simply control whether there is a negative sign or not, we would have two binary numbers that both represent zero - 10000000 (negative zero) and 00000000 (positive zero). To avoid ambiguity, along with a variety of other reasons, computers represent negative numbers in two's complement. If the sign bit is 1, then invert all bits (i.e. 1 is considered a 0, and 0 is 1) and add 1 to the sum to get the negative number.