Question

You are asked to design a system of FP numbers representation (with your own design choices), labeled Custom_FP_48, for which we have 48 bits at our disposal in order to represent a number, in analogy with the IEEE 754 prototype. You are asked to provide: a) The types for evaluating this number b) The width of representation of these numbers (upper and lower) 6 c) The maximu

Answer 1

Answer:

Check the explanation

Explanation:

The most significant bit is the sign bit (S), with 0 for positive numbers and 1 for negative numbers.

   Normalize significand: 1.0 ? |significand| < 2.0

       Always has a leading pre-binary-point 1 bit, so no need to represent it explicitly (hidden bit)

   The following 9 bits represent exponent (E).(0 TO 511)

       E is : actual exponent + Bias

       Bias = 255;

   The remaining 38 bits represents fraction (F).

Width of representation

smallest value :

   Exponent: 000000001 because 000000000 is reserved

       actual exponent = 1 – 255 = –254

   Fraction: 000…00  \rightarrow significand = 1.0

Kindly check the attached image below to see the concluding solution to the question above.