1. If Denormalization is used how many additional numbers can be represented?

a. What is the smallest positive number now?

b. What are Zero(s)?

2. Compare the above 8-bit FLP representation and 8-bit 2s complement representation in terms of the range and accuracy of integer representations (are they both represent equal number of real numbers?).

3. Do Q3 & Q4, but assume now that the computer uses 8-bit for FLP (1bit for sign, 5 bit for exponent with excess-3 rep., rest for magnitude). Assume 00000 and 11111 in exponent field are reserved for denormalization.

4. Assume a compiler represent very small flp (say vsflp) as 8-bit .

Suppose variables W, X, Y, and Z are initialized as follows (type vsflp).

Vsflp x = 12, y = 4.5

a. How X, Y and Z will be represented?

b. Show how the following operations will be calculated by the FLP unit?

X + X, X + Y, Y + Y

c. Which of the above operations will overflow or loose precision?

d. Show how X*Y will be calculated (assume intermediate calculations will be done in 8-bit register). Write an algorithm to demonstrate this operation.

e. Show how X/Y will be calculated.

c. Show how (X / 0 ) , ( 0/ X) and ( 0 / 0 ) will be represented?

5. Consider the program below.

#include

int main(void)

{

int I = 16777217;

float F = 16777216.0;

printf("The integer is: %d ", I);

printf("The float is: %f ", F);

if (I == F) printf("They are equal);

}

What will be printed? Explain.