Assignment # 1 CSE 330(01)
Instructions for preparing the solution script:
• Write your name, ID#, and Section number clearly in the very front page.
• Write all answers sequentially.
• Start answering a question (not the pat of the question) from the top of a new page.
• Write legibly and in orderly fashion maintaining all mathematical norms and rules. Prepare a single solution file.
• Start working right away. There is no late submission form. If you miss the deadline, you need to use the make-up
assignment to cover up the marks.
1. In the classes, we discussed three forms of floating number representations as shown below,
Lecture Note Form : F = ±(0.d1d2d3 · · · dm)β β
e
, (1)
Normalized Form : F = ±(1.d1d2d3 · · · dm)β β
e
, (2)
Denormalized Form : F = ±(0.1d1d2d3 · · · dm)β β
e
, , (3)
where di
, β, e ∈ Z, 0 ≤ di ≤ β − 1 and emin ≤ e ≤ emax. Now, let’s take, β = 2, m = 4 and −3 ≤ e ≤ 6. Based on
these, answer the following:
(a) (4 marks) What are the maximum numbers that can be stored in the system by the three forms defined above?
(b) (4 marks) What are the non-negative minimum numbers that can be stored in the system by the three forms
defined above?
2. Let β = 2, m = 4, emin = −1 and emax = 2. Answer the following questions:
(a) (4 marks) Compute the minimum of |x| for normalized form.
(b) (4 marks) Compute the Machine Epsilon value for the denormalized form.
(c) (4 marks) Compute the maximum delta value for the form given in Eq.(1).
3. (10 marks) Let f(x) = e
x − sin(x) + x − 1. To evaluate f(x) near zero we need to compare f(x) to the Taylor
expansion of f(x) at x = 0. Evaluate the Taylor coefficients, a0, a1, a2, if we compare f(x) with degree two
polynomial near zero.
Motto: Mathematics is NOT difficult, but what is difficult is to believe that mathematics is NOT difficult.
