Bytes, Bases, and Internal Representations

  1. The typical sizes of various types of data are given below. Find the number of bits needed to store each. You may assume the below use the traditional computer science definitions ($1$ kB = $1024$ bytes, $1$ MB = $1024$ kB, etc...).

    1. Word document - $30$ kB
    2. Photo - $2.9$ MB
    3. Movie on a DVD - $4.3$ GB
    4. Windows 8 Installation - $8$ to $11$ GB
    5. The entire internet - $5,000,000$ TB
  2. Can you store a video file that is $3.9$ GB bytes large on your thumb drive, which according to the drive manufacturer has a capacity of $4$ GB? (Recall how a drive manufacturer's concept of a gigabyte sometimes differs from others...)

  3. For each, determine what the value would be in the indicated form.

    1. $15$ in binary
    2. $101_{10}$ in base $2$
    3. $10101011_2$ in decimal form
    4. $1023$ in hexadecimal
    5. $1021_7$ in base $13$
    6. $10001001_2$ in hexadecimal
    7. $1021_8$ in base $16$
  4. Convert the decimal numbers $315$ and $440$ into binary. Suppose we attempt to store each binary value into a single byte, dropping the left-most bits as necessary to make it fit. That is to say, remove all but the last (right-most) 8 digits. Convert the resulting bytes into decimal numbers. In what way do the resulting numbers relate to the original numbers? Are they less or greater than the original? By how much? Why?

  5. Convert the following integers to 8-bit Two's Complement form:

    1. $105$
    2. $-73$
    3. $-128$
  6. Convert the following decimal values to IEEE-754 form:

    1. $0.35$
    2. $13.796$
    3. $-0.001$
  7. The characters of a string of text have the following ASCII values, respectively: 89, 111, 117, 114, 32, 115, 111, 108, 117, 116, 105, 111, 110, 32, 105, 115, 32, 99, 111, 114, 114, 101, 99, 116, 33, 46. What was the original string of text?

  8. Encode the text "ASCII is easy" in ASCII values (without the quotes).

  9. Briefly describe the main limitation of ASCII and how Unicode addresses it.