Suppose a new standard, the IDDD-643 standard, is developed for storing numbers in a string of 16 bits. The first bit is used for the sign of the number (0 if positive and 1 if negative). The next 5 bits store the exponent plus the bias, and the remaining 10 bits store the mantissa. The bias is 15 and no bits are reserved for any special purposes.

1) Write a number 581 in the 16-bit IDDD-643 standard. If you use MATLAB as your calculator, please type in format long command first. That is, a fraction number must be represented by at least 15 digits. For example, 13/11 should be displayed as 1.181818181818182 instead of 1.1818.

2) Carefully calculate the round-off error?