If the distance between 7 and the next larger floating-point number is 2^-12. What is machine epsilon on that computer? What is the distance between 70 and the next larger floating-point number on that com- puter? Assume of course that the computer represents numbers in base 2.
-Should the machine epsilon just be 2^-12? -since machine epsilon is the smallest floating point between two number, so does it change between 70 and next number?
Machine precision epsilon is usually the smallest epsilon that we can add to 1 such that it is distinct.
7 is encoded as $.111\times 2^3$ while 1 is encoded as $.1\times 2^1$.
Since $2^{-15}\times 2^3=2^{-12}$ we must have that $\epsilon=2^{-15}\times 2^1=2^{-14}$. It also means that we have a mantissa of 15 bits.