CSE 2312 - Assignments - Assignment 4

The assignment will be graded out of 100 points. Submit a document entitled answers.xxx (where you replace xxx with whatever extension is appropriate, depending on the file format you use), that contains your answers. Acceptable file formats are plain text, Word document, OpenOffice document, and PDF. Put your name and UTA ID on the first line of the document.

Submit your document to Blackboard before the deadline. You will be able to revise your answers until the deadline with no penalty.

Task 1 (10 points)

What is the largest number that can be stored as an 8-bit integer? Why?

Task 2 (10 points)

Convert decimal number 19 to binary.

Task 3 (10 points)

Convert binary number 101001 to decimal.

Task 4 (10 points)

Let L be any high-level programming language (existing or possible) that we can run on a modern computer. Under what cases is it mathematically possible to design a computer that uses that language as its microarchitecture-level language? Always, sometimes, never? Justify your answer. If you answer "sometimes", be specific about when it is possible and when it is not possible.

Task 5 (20 points)

Part a (10 points): The inhabitants of Planet Iris have an alphabet of 28 symbols (this includes punctuations, spaces, everything else you could possibly need to represent text). Assuming that each symbol is assigned a specific binary pattern, how many bits do you need per symbol?

Part b (10 points): For storing text from planet Iris, suppose that we want to use memory as efficiently as possible, by assigning long binary codes to strings of symbols, as opposed to assigning short-term binary patterns to individual symbols (which was the case in part a). What is the least amount of memory (in bits) needed to store an arbitrary string whose length (in the Iris alphabet) is 57 characters? Note: the alphabet still has 28 symbols. The string contains 57 of those symbols.

Task 6 (20 pts.)

Determine if it is possible to have an error correction method that: If it is possible, define the mapping of each 2-bit word to a codeword. If it is not possible, explain why not.

Task 7 (10 pts.)

(This is Problem 8 from Chapter 2 of the textbook).

Compute the data rate of the human eye using the following information. The visual field consists of about 106 elements (pixels). Each pixel can be reduced to a superposition of the three primary colors, each of which has 64 intensities. The time resolution is 100 msec.

Task 8 (10 pts.)

(This is Problem 9 from Chapter 2 of the textbook).

Compute the data rate of the human ear from the following information. People can hear frequencies up to 22 kHz. To capture all the information in a sound signal at 22kHz, it is necessary to sample the sound at twice that frequency, that is, at 44 kHz. A 16-bit sample is probably enough to capture most of the auditory information (i.e., the ear cannot distinguish more than 65,535 intensity levels).

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