1) Assuming integers are represented as 16-bit words and negative numbers are represented using the 2's complement representation, convert the following hexadecimal numbers to decimal numbers (show your work).
a. FEED, b. BAD1, c. 2DAD
2) Assuming integers are represented as 32-bit words and negative numbers are represented using the 2's complement representation, convert the following decimal numbers to hexadecimal numbers (show your work).
a. -1954, b. 15343
3) Represent following floating point numbers in IEEE single-precision (32-bit) format: a. -0.1875, b. 0.46875
Show the steps done to reach the answer for each (i.e. how to get the S-bit, the exponent, and the fraction field of the answer).
4) What is the decimal value of the following IEEE single-precision (32-bit) floating point numbers (which are shown in hexadecimal)?
a. 3F400000, b. BE000000
Show the steps done to reach the answer for each.
Note: Do NOT omit the leading zeros (Os) in your answers.
Write code for an Θ(n) worst-case algorithm that verifies that a tree is actually an AVL tree. You may assume the nodes of the tree look like:
1. class AVLNode
2 int key:
3 v value;
4 int height;
5 AVLNode Left:
6 AVLNode right;
You must verify the BST Property, the AVL Balance Condition, and the correctness of the height information (that is, the value stored in the height field may not be correct). In each of the cases where it fails a property, return false. Otherwise, return true. A null node is considered a proper AVL tree of height -L You are welcome to (encouraged!) to write helper functions.
As you are writing your code, we recommend that you keep in mind the following tree. Is THIS tree a proper AVL Tree?
