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Introduction

The course syllabus gives the reading assignments for the course. This homework assignment should covers the Background_Material web page. If you do not have a copy of the textbook yet (be sure to get the Fourth Edition), you can still do this assignment.

The Assignment

After reading the background material, answer the following questions:
  1. How many orders of magnitude bigger than a fluid ounce is a gallon?

    There are 128 fluid ounces in a gallon. The log10(128) is 2.107, so a gallon is two orders of magnitude larger than a fluid ounce.

  2. How many orders of magnitude bigger than a kilogram is a milligram?

    A kilogram is 103 grams, and a milligram is 10-3 gram; +3 − (−3) is 6, so a kilogram is six orders of magnitude larger than a milligram.

  3. How many picoseconds are there in a nanosecond?

    1,000

  4. How many nanoseconds are there in a millisecond?

    1,000,000

  5. I am thinking of a number between 1 and 100. On average, how many yes-no questions would you have to ask to find out what my number is?

    The log2(100) is 6.644, so that is the average number of questions. You could always get the answer with 7 questions, but sometimes it would take only 6; 6.644 would be the average of all the 6's and 7's if we played the guessing game lots of times.

  6. There are 23 bits in a byte. How many bits are there in a gigabyte of memory?

    23 × 230 = 233 bits.

  7. How many bits of storage are there in a 256GB disk drive?

    28 × 109 × 23 = 211 × 109 = 2,048,000,000,000 bits.

  8. How many different values can be representd in a byte of memory?

    28 = 256 different values.

  9. How many bits would it take to represent a number between 1 and 256G?

    38

  10. How many bits would it take to represent a number between 0 and one less than 64M?

    26

  11. What is the 6-bit two’s complement representation of +1810?

    010 0102

  12. What is the 6-bit two’s complement representation of -1810?

    101 1102

  13. What is the 12-bit two’s complement representation of -1810?

    111 111 101 1102

  14. What is the result, in binary, of negating your answer to the previous question?

    000 000 010 0102

  15. To convert feet to inches, do you mulitply the number of feet by 12 or do you divide by 12?

    multiply

  16. Is one nanosecond 1,000 picoseconds, or is it 0.001 picosecond?

    1,000 picoseconds

  17. How many picoseconds in one-eighth of a nanosecond?

    1000 ÷ 8 = 125 picoseconds

  18. How many picoseconds in eight nanoseconds?

    8,000 picoseconds

  19. What is the period of a 1 Hz signal?

    1 second (Don’t forget to specify the unit of measure!)

  20. What is the period of a 1 KHz signal?

    0.001 second = 1 millisecond

  21. What is the frequency of a signal with a 2 nsec period?

    1 ÷ (2 × 10−9) = 0.5 × 109 = 500 × 106 = 500 MHz

  22. What is the frequency of a signal with a 200 psec period?

    1 ÷ (200 × 10-12) = 0.005 × 1012 = 5 × 109 = 5 GHz

  23. What is the period of a 2.5 GHz signal?

    1 ÷ (2.5 × 109) = 0.4 × 10-9 = 400 × 10-6 = 400 µsec

  24. How long does it take a 7200 RPM disk to make one revolution? Give your answer in milliseconds and also in microseconds.

    7200 RPM = 120 revolutions per second. 1 ÷ 120 = 0.00833… sec = 8.333 msec = 8,333 µsec

  25. What is the decimal equivalent of binary 1111011.01110100? (Answer to two decimal places.)

    Hexadecimal shortcut: 7B.74 = 7 × 161 + 11 × 160 + 7 × 16-1 + 4 × 16-2 = 112 + 11 × 0.0625 + 4 × 0.0039525 = 123 + 0.4375 + 0.015625 = 123.4510

  26. What is the unsigned binary representation of decimal 7.25?

    0111.01

  27. What is the binary representation of negative 4 using 8-bit bias-127 notation?

    127 - 4 = 123 = 0111 1011

  28. What is the result of negating the 4 bit two’s complement number 01012? Answer in both binary and decimal.

    10112 = -510

  29. What is the result of negating the 4 bit two’s complement number 00002? Answer in both binary and decimal.

    00002 = 010

  30. What is the result of negating the 4 bit two’s complement number 10002? Answer in both binary and decimal.

    10002 = -810