COS 111, Fall 1999 - Problem Set 3

Due by 5pm, Tuesday Oct. 12, 1999

Problem 1
"CD quality" sound is represented by using 2 channels (stereo) and for each channel taking 44,100 samples per second and using 16 bits per sample. Another alternative is "radio quality" sound. This representation uses only one channel (mono) at a sample rate of 22,050 samples per second and only 8 bits per sample. Approximately how many hours of sound recording can be stored in on a 1 Gigabyte disk in each of CD quality and radio quality representation? A 1 Gigabyte disk can hold approximately 8 billion bits.

Problem 2
Give the table of values (called the truth table) for the following Boolean expression

     (x or y) and (!x or !y)
Do you recognize this function?

Problem 3
The truth table below shows the value of the carry bit resulting from the addition of 3 operand bits: x, y, and z. Write an expression using AND, OR, and NOT to represent the carry bit function.

           x y z | carry(x,y,z)
          -------|-------------
           0 0 0 |    0
           0 1 0 |    0
           1 0 0 |    0
           1 1 0 |    1
           0 0 1 |    0
           0 1 1 |    1
           1 0 1 |    1
           1 1 1 |    1

Problem 4
How many different Boolean functions of two variables are there? Equivalently, how many ways are there to fill in the truth table below?
           x y  | f(x,y)
          ------|---------
           0 0  |    
           0 1  |    
           1 0  |    
           1 1  |    

Problems 5 - 7 From Brookshear, Chapter One Review Problems (pg. 73):
31,
32,
33-b


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