Quiz 1 Solutions

Mon Feb 2

You have up to 25 minutes. You may use a standard calculator, but no text book or notes.

  1. Suppose we have the digits 152, written using base six. What quantity does that represent, expressed in base ten? +2

    The column values in base six are (left to right) 36, 6, and 1. So this number is 1×36 + 5×6 + 2×1 = 36 + 30 + 2 = 68.

  2. Convert the following unsigned binary numbers into base ten. +4

    1. 11100    = 28
    2. 11011    = 27
    3. 11001    = 25
    4. 111    = 7

  3. Convert the following base ten numbers into binary using 5-bit signed two’s complement +4

    1. \(-12\)    = 10100
    2. \(13\)    = 01101
    3. \(-8\)    = 11000
    4. \(-1\)    = 11111

  4. Add and verify the following unsigned (not fixed-size) binary numbers. +4

    We keep the extra carry bit, because these are not fixed width!

        1 1                          1 1 1 1           
      1 1 0 0  = 12                  1 1 1 1 1  = 31
+ 1 0 0 1 1 0  = 38              + 1 0 0 1 0 0  = 36
——————————————                   ——————————————
  1 1 0 0 1 0  = 50              1 0 0 0 0 1 1  = 67

  5. Convert the hexadecimal number 27C to binary. +3

    0010 0111 1100

  6. Convert the octal number 615 to binary. +3

    110 001 101