I'm reading the book A First Course in Numerical Methods by U. Ascher and C. Greif, and in the 2nd chapter it's written that ... we associate $x$ a floating point representation $fl(x)$ of the form similar to that of $x$ but with only t digits, so$$fl(x) = sing(x) \times (1.d_1d_2d_3 \cdots d_{t-1}d_t) \times 2^e$$Then it says that the relative error $$\frac{fl(x) - x}{|x|}$$ is bounded by $n = \frac{1}{2} \times 2^{-t}$.So for a double-precision floating pointer number (represented using IEEE), which uses $52$ for the mantissa, $n = 2^{-53} \times 1.1 \times 10^{-16}$Why $-53$ if the mantissa of a double floating point number is $t = 52$? 
t digits are used to represent the mantissa in floating-point system, but rounding unit is calculated for doubles with 53 bits
floating point;numerical