Computer Architecture

Chapter 1 Solutions:

• 1. Describe the difference between a digital and analog signal. Give an example of each type.
• 2. How many different values can be represented with a single binary digit? List the possible values.
  Two values. 0 and 1.


• 3. How many bits are in a byte?
  Eight bits per byte.


• 4. How many bits are in a Megabyte (MB)?
  There are 1024*1024*8 = 8388608 bits per Megabyte.


• 5. How many Megabytes are in a Gigabyte (GB)?
  There are 1024 Megabytes in a Gigabyte.


• 6. How many distinct values can be represented by a Byte? Two Bytes?
  A byte can represent 256 distinct values. Two bytes can represent 65536 distinct values.


• 7. Suppose you are designing a controller for a new game system. Describe a digital encoding for the direction pad that only uses, at most, four bits. Note that there are 9 possible directions: up, down, left, right, up left, up right, down left, down right, and centered.
  

  Binary code	Description
  0000	up
  0001	down
  0010	left
  0011	right
  0100	up left
  0101	up right
  0110	down left
  0111	down
  1000	right
  1001	centered



• 8. Determine the number of combinations that can be represented using the following number of bits.
  • A) 1
    2 combinations.
  • B) 8
    256 combinations.
  • C) 10
    1024 combinations.
  
  
• 9. Determine the minimum number of bits required to represent the following numbers
  • A) 34
    6 bits.
  • B) 67
    7 bits.
  • C) 93
    7 bits.
  
  
• 10. Convert the following decimal numbers into binary using the division method.
  • A) 100
    1100100b.
  • B) 256
    100000000b.
  • C) 63
    111111b.
  • D) 30
    11110b.
  
  
• 11. Converrt the following decimal numbers to hexadecimal using the division method.
  • A) 101
    0x65
  • B) 57
    0x39
  • C) 21
    0x15
  • D) 17
    0x11
  • E) 257
    0x101
  • F) 31
    0x1F
  
  
• 12. Convert the following hexadecimal numbers to decimal.
  • A) 0x7E0
    2016
  • B) 0xA11
    2577.
  • C) 0xCAB
    3243.
  • D) 0x80F
    2063.
  • E) 0x942D
    37933.


• 13. Convert the following binary numbers to decimal and hexadecimal.
  • A) 0101b
    5, 0x5.
  • B) 11010011b
    211, 0xD3.
  • C) 00000001b
    1, 0x1.
  • D) 10b
    2, 0x2.
  • E) 1100b
    12, 0xC.
  • F) 11111111b
    255, 0xFF.


• 14. Convert the following hexadecimal numbers into binary using the minimal number of bits possible.
  • A) 0xFACE
    1111101011001110b.
  • B) 0x1234
    1001000110100b.
  • C) 0xB1DE
    1011000111011110b.
  • D) 0xF00D
    1111000000001101b.
  • E) 0x1F
    11111b.