CZ1101, Tutorial 4, Week 11, 22-27 September, 1997

You should hand in the solutions to problem 2 and 6 in the tutorial class. Do other problems as well if you can.

  1. (4.10) [5] What hexadecimal number does this binary number represent? 
    1100 1010 1111 1110 1111 1010 1100 1110
  2. do* (4.1) [25] The Big Picture on page 243 of the textbook mentions that bits have no inherent meaning. Given the bit pattern 
    1000 1111 1110 1111 1100 0000 0000 0000
    What does it represent, assuming that it is
  3. (4.21) [10] Find the shortest sequence of MIPS instructions to determine the absolute value of a two's complement integer. I. e., convert this instruction (accepted by the MIPS assembler): 
    abs  $10, $11   # $10 = |$11|
    This instruction means that register $10 has a copy of register $11 if register $11 is positive, and the two's complement (negatived value) of register $11, if $11 is negative.
  4. (4.28) [5] The full MIPS instruction set has two more logical operations not mentioned thus far: xor and nor. The operation xor stands for exclusive OR, and nor stands for not OR. The table that follows defines these operations on a bit-by-bit basis. 
         a     b      a xor b      a nor b
     0     0         0            1
     0     1         1            0
     1     0         1            0
     1     1         0            0
    Show the minimal MIPS instruction sequence for a new instruction called not that takes the one's complement (invert 0 and 1) of a source register and places it in a destination register. Convert this instruction (accepted by the MIPS assembler). 
    not  $10, $20
    The not operation in C is the operator `!'.
  5. [15] Write in 6-bit two's complement representation of the integers a=29, b=31, c=-31. (a) Calculate (paper-pencil longhand way) a+b, a-b, b-a, a+c, a-c, and c-a in two's complement arithmetic. Indicate if overflow occurs. (b) Similarly, compute a*b, a*c, b*c, and b/a.
  6. do* [10] Compute the product of two 5-bit binary numbers, 10101*01011: