How do we distinguish positive and negative integers? The first bit (leftmost bit) is called the sign bit and it determines the sign. 1 for negative, 0 for positive
This gives one less bit to store the values of integers; effectively reduces the range of positive values by one-half; this can be overcome
Negative numbers use two's complement representation; that's why when you add 1 to 127, the result is -128!
Fractions use same notation as decimal except instead of each decimal place being 10-1, 10-2, 10-3, etc., it's 2-1, 2-2, 2-3, etc. (i.e. 1/2, 1/4, 1/8) so 6.75 is represented as 110.11
Internally, fractions (floating point numbers) are really stored in a more complex way, but the notion is the same
Due to the amount of bits available for storing numbers, computers have round-off errors;
You as the programmer must be aware of the computer's limitations with data representation and storage