Homework 4: Boards and Circuits

• Get started using circuit simulation software to implement circuits.
• Explore the computations involved in performance.

1. [1 points] Using TKGate or Digital, implement a circuit that computes the and of two inputs.
2. [3 points] Using TkGate or Digital, implement a circuit that demonstrates the function of a 4 input multiplexer.
3. [6 points] Using either TKGate or Digital, implement a WOMBAT program counter.
   • The PC can use a word of 8 bits instead of 16.
   • Your circuit should have the following inputs, all labeled
     • Bus a word sized input representing the value of the bus.
     • PCFromBos a one bit input
       • when set to 1, the value from BUS will be the source for the register,
       • when 0 the value of PC+2 will be the source for the register.
     • LoadPC when this goes from 0 to 1, the appropriate value will be stored in the register.
     • In addition, if you implement in TKGate, you should have a reset line which resets the register.
   • Your circuit should have the line that would normally be output to the bus connected to a display which shows the current value of the PC.
   • The following images are examples of I/O with the circuit blacked out.
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4. Two processors, P₁ and P₂, executing the same instruction set have the following performance:

   Processor	Clock Speed	CPI
   P1	2.4 GHz	3
   P2	2.9 GHz	3.3

   Answer the following by showing all work:
   1. [2 points] What is the speed of each processor in seconds per instruction.
   2. [2 points] What is the performance of each processor?
   3. [1 point] How much faster is P₂ than P₁
5. If P₁ from the previous problem has three classes of instructions, with an instruction mix as follows

   Class	CPI	Percent Used
   A	1	25%
   B	3	25%
   C	4	50%

   Assume you are modifying the compiler and can rearrange the instruction mix by changing the instructions called by your program. Assume the number of instructions is fixed (probably unrealistic in this case).

   Answer the following by showing all work:

   1. [1 point] Verify that the CPI for the above instruction mix is 3.0
   2. [2 points] By shifting instructions from class C to class A what would the new instruction mix need to be so that P₁ has roughly the same performance as P₂?
      You should be able to do this mathematically, but you may set up a spreadsheet and guess and check if you wish. In either case, indicate how you solved the problem.
   3. [2 points] Why is this not likely to be possible to accomplish this task by only shifting instructions?

Submission

• A single file containing all circuits should be submitted to your instructor by email before class begins on the due date.
  • This should be either a .v file for TKGate or a .dig file for Digital.
• If you choose to solve problems 4 and 5 using a spreadsheet
  • Make sure that the computations are well labeled.
  • Attach a version of this spreadsheet in Microsoft excel format to the email containing the circuits.
• If you choose to solve problems 4 and 5 on paper, submit a typed hard copy of the solution at the beginning of class on the due date.