Comment your code, and explain your answers clearly. Have fun.

1. (15 points) Write a PDP8/E subroutine (called with JMS, not via our CALL and RETURN mechanism) to compute A mod B. More specifically, when the subroutine is called, the AC should contain the address of two consecutive data words, A and B. These words should be interpreted as non-negative 12-bit integers. When the subroutine returns, the AC should contain A mod B.

   Since we're considering 12-bit non-negative integers, you need not worry about the signs of A and B. However, you should return 0 if B is 0.

   Don't try to get fancy. You can compute A mod B by subtracting B from A repeatedly until the remainder is less than B.
   
   

2. (10 points) The table below lists execution times for all the PDP8/E instructions we have used. Please answer the following questions.
   • Does the notion of CPI make sense in the context of the PDP8/E? Why or why not?
   • Even if you said CPI does not make sense, you can still use the timing table below to compute the native MIPS for the PDP8/E if you first make some assumptions about the frequency with which the various sorts of instructions are executed during the run of a typical PDP8/E program. Write down and argue briefly for your best guesses as to instruction class frequencies.
   • Using your instruction class frequency estimates and the timing table below, compute the native MIPS for the PDP8/E.
   • Based on what you know about modern workstations, how does the MIPS rating of the PDP8/E compare to modern machines?
   
   
   

   
   Execution times in micro-seconds for PDP8/E instructions
   --------------------------------------------------------
                            Addressing mode     
                 ------------------------------------------
   Instruction                            Indirect with
      Type       Direct      Indirect     auto-increment
   --------------------------------------------------------
   AND            2.6          3.8             4.0
   TAD            2.6          3.8             4.0
   ISZ            2.6          3.8             4.0
   DCA            2.6          3.8             4.0
   JMS            2.6          3.8             4.0
   JMP            1.2          2.4             2.6
   
   Opcode 7          1.2 (addressing mode irrelevant)
   --------------------------------------------------------
   

   
   
   
3. (3 points) We have a new male kitten at our house. What should we name him?
   
   
4. (10 points)
   • Draw a 3-bit adder. This circuit should have six input lines corresponding to the two 3-bit numbers we want to add, and four output lines, corresponding to the (possibly) four digits of the sum. The fourth output line is usually referred to as the "carry" or "carry out" of this circuit.
   • Suppose every gate in your 3-bit adder has a propagation delay of 8 nanoseconds (ns). What is the propagation delay of the entire circuit? That is, how long after all six input values are stable do you have to wait before you can count on all four output values being correct?
   • If you extend your 3-bit adder to an N-bit adder, what is the propagation delay of the resulting circuit?
   
   
   
5. (10 points)
   • Suppose you have a trailing-edge-triggered JK flip-flop, and you wire the J and K inputs both to 1. If the clock line goes up and down repeatedly and regularly, what happens to the output Q of the flip-flop?
   • Keep the flip-flop from the previous part wired as before, and call its output line Q0. Suppose you have two more flip-flops of the same type, with output lines Q1 and Q2, respectively. How can you connect these two new flip-flops to the original one in such a way that as the clock line entering the first flip-flop ticks and tocks, the 3-bit binary number Q2 Q1 Q0 cycles through the numbers ...000, 001, 010, 011, 100, 101, 110, 111, 000, 001,...? That is, how can you hook three flip-flops to a clock to make a 3-bit counter?