Description
Theoretical Assignment 1: Suppose we have a decimal number (−28.91)10
1. Convert it to binary number, show the specific procedures, and truncate
the result with accuracy to 4 decimal places. (Points: 25)
2. Convert your binary number back to its corresponding decimal number,
show the specific procedures, and evaluate the relative error. (Points: 15)
3. Use online calculator1
to present the floating point representation of (−28.91)10
in a 32-bit computer. Show the specific sign(s) (1-digit), exponent(n) (8-
digit), and Mantissa (f) (23-digit). (Points: 10)
1
see a useful website: https://www.h-schmidt.net/FloatConverter/IEEE754.html
1
Theoretical Assignment 2: Suppose we have a matrix A:
A =
2 1 0
1 4 0
0 3 10
(1)
1. Find the L1 and L∞ norms of A (Points: 15)
2. Show the details of evaluating eigenvalues of A, the L2 norms of A and
A−1
. Numbers you may need: √
2 ≈ 1.414 and √
8 ≈ 2.828.
Note: use pre-programmed functions such as ’eig’ in MATLAB, ’eigenvalues()’ in C++, and ’eigvals’ in Python would get few credits. (Point:
25)
3. Evaluate the condition number of matrix A based on the resulting L2
norms of A and A−1
(Point: 10)
Note: use pre-programmed functions, such as ’cond’ in MATLAB and the
like, would get few credits.
