Quiz 2

1. Based on the circuit below, fill in the “Out” column of the truth table. Use the dropdowns to select your answers. For example, if the cell with a (1) should be filled in with a 0, use the dropdown to select (1) = 0.

   

   • Answer

     

2. 

   • Answer

     Sum of product simplification:

     A'BC + ABC' + AB'C' + AB'C

     =A'BC + AC'(B + B') + AB'C

     =A'BC + AC' + AB'C

     =A'BC + A(C' + B'C)

     =A'BC + A(C' + B')

     =A'BC + AC'+AB'

     

3. What is the gate depicted in the first image? What type of gate can we replace mystery with in the second image to create a NOR gate?

   

   • Answer

     1. NAND

     2. AND

4. a. In order for a multiplexer to have 33 inputs, how many selector bits does it require?

   b. If a decoder has 6 selector bits, what is the maximum number of output lines that it can have?

   • Answer

     1. 6 (2^5 = 32 < 33)

     2. 2^6 = 64

6.

00, 11, 10, 01

• Answer

  11

  Selector: 00 Mux: 01

  Selector: 01 Mux: 10

  Selector: 10. Mux: 00

  Selector: 11 Mux: 11

8. Classify the following circuits. If a circuit can be implemented using only combinational logic, it should be classified as combinational. If it requires the use of sequential logic, it should be classified as sequential.

   

   Combinational Logic:

   Sequential Logic:

   • Answer

     Combinational: C, F, E, Multiplexer, 8-bit Subtractor, XOR gate

     Seuqntial: B, D Flip Flop, Instruction Register in LC-3, Microcontroller(state machine) in LC3, RS Latch

9. 

   • Answer

     Level Triggered

10. You are given a system with 18-bit addressability which uses 8 bits to represent its memory addresses. How much memory is this system able to address, in bits?
    • Answer

      2^8 * 18 = 4,608

11. [B] The circuit below implements a one-hot state machine. Your task is to fill in the blanks to recreate the state diagram of the state machine. Utilizing the circuit below, select an option for each numeric dropdown for what you think would go in that position in the state diagram (also shown below).

    

    

    • Answer

      

12. 

    • Answer

      

13. Fill in this K-map according to the truth table above. Use the dropdowns to select your answers. For example, if the cell with a (1) should be filled in with a 0, use the dropdown to select (1) = 0.

    

14. From the above K-map, give the minimally reduced boolean expression in sum-of-products form. Don't add any spaces in your answer, and follow the S1/S0/G order of the headers for each term: e.g. "S1S0G+S1'G''" instead of "GS0S1 + G'S1'".

    

    • Answer

      S1'S0'G'+S1G

15. In the LC-3, what is stored inside of the IR? What is stored inside of the PC?
    • Answer

      IR holds the value of the current instruction, whereas PC holds the current PC address of the next instruction to execute.