(50 points) Suppose a new standard, the IDDD-643 standard, is developed for stor

Question

(50 points) 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.

2) Calculate the round-off error?

Explanation / Answer

Solution to part 1:

Binary representation of 581 : 1001000101

This can be represented as 1.001000101 x 10^9

So, number is positive hence 1st bit is 0.

Bias + Exponent = 24 ie 11000.

Mantissa is 1.001000101. Since,the most significant bit before the radix will always be 1 hence out mantissa bits are 1001000101, ie we don't need to represent the position of the radix.

so final IDDD-643 standard number is : 0 11000 1001000101

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