Contents:

• Overview
• Practice Problems
• Problems to be Submitted

Topic: Operating on binary integer numbers. Arithmetic (+, -, *, /, %), Boolean (&, |, ^, ~), and shifts (<<, >>)
Related Reading: Sections 5.2, 6.2, and class notes

• Solutions to the odd-numbered problems at the end of Chapters 5 and 6 are available on the textbook's companion website.
  

You are allowed to submit your assignment via email, but if you choose to do so, you must bring a hardcopy of your assignment along with a completed cover sheet to the instructor at the next class. (Note: Do not email the instructor any .zip file attachments, as SLU's email may not accept these emails; i.e. the instructor may not receive your email.)

1.   (10 points)    Operations on Data:

     Given the following variable declarations:

        short a = 0b0010101100011001;
        short b = 0b0101100110101011;
        short c = 0b1111111101110010;
   
        unsigned short j = 0x95;
        unsigned short k = 0xF35C;
   
        int n = 0xA39D2;
        int p = 0x5A48;
   

     Compute results for the following data operations.

           Be sure to show your work, and please give your answer in binary or hex

   1.    a   +   b
   2.    n   ‐   p
   3.    b   &   c
   4.    n   ^   p
   5.    a   <<   7
   6.    k   >>   6
   7.    c   >>   5
   8.    (23   <<   4) ‐ 0xFF
   9.    j % 6
   10.    ((a + b < c) || ((p < n) && !(j % 2)))

2.   (6 points)    Shifts and Bit Manipulation for Fast Multiplies and Divides:

   Assume for the following problems that x and y have been declared as follows:

       short x, y;
   

   Note:  x can be any value that results in valid value for y.

   1.   The following code corresponds to the mathematical equation: y = K * x, for some fixed value of K. In this case, what is K?

         x = 13
         y = (x << 3) - x
   

   2.   The following code similarly corresponds to: y = K * x, but for what value of K?

         x = 6
         y = x + (x << 1) - (x << 4)
   

   3.   The following code corresponds to the mathematical equation: y = K * x, for some fixed value of K < 1. What is the value of K?

         x = 22
         y = (x >> 2) + (x >> 3)
   

   4.   Relative to multiplication and division, what mathematical equation does the following code produce?

         x = 117
         y = x & 0x0f
   

3. (9 points)

   Using the diagram of the ALU from Figure 5.17 in the textbook, displayed here or downloadable here:

   

   Indicate what the 32-bit Result output, and each of the 1-bit Zero, Negative, and Carry outputs, would be for each of the following sets of inputs:

   1.   A = 0x3D56B,   B = 0x28C5,   ALUControl_1:0 = 11
   2.   A = 0x3D56B,   B = 0x28C5,   ALUControl_1:0 = 00
   3.   A = 0x28C5,   B = 0x28C5,   ALUControl_1:0 = 01
   4.   A = 0x3A5,   B = 0xC48,   ALUControl_1:0 = 10
   5.   A = 0x3D56B,   B = 0x28C5,   ALUControl_1:0 = 01
   6.   A = 0xFFF3D56B,   B = 0xFFFF28C5,   ALUControl_1:0 = 10