Assignment submission:

Problems should be neatly presented on paper. Hand in, or place under my door.

Questions:

1. (10 marks) Draw the digital circuit that takes three input values b1, b2, b3, and computes two output bits s1, s0, where if s1 s0 were read as a binary number, it would represent the sum of the three input bits. That is, if the three input bits are all ON, then the output bits are s1 s0 = 11. If any two of the input bits are ON, and the other one OFF, then the output bits are s1 s0 = 10.
   [Note: the output bit s0 is ON if and only if an odd number of the input bits are ON, so you may be inspired by the Lab1 circuitry you came up with. It is acceptable to use Logisim to come up with the circuitry, but note that you will have to come up with circuits on tests and exams without Logisim.]
2. (5 marks) Give a Karnaugh map for the following boolean function, and give the "Sum of Products" (i.e., "OR" of "AND" gates) boolean formula that minimizes the number of gate inputs -- but you should not count negated literals (i.e., ¬ x) as a gate input: we get negated literals "for free".

   wxyz |   R
   0000 |   1
   0001 |   0
   0010 |   1
   0011 |   1
   0100 |   X
   0101 |   X
   0110 |   0
   0111 |   0
   1000 |   X
   1001 |   0
   1010 |   1
   1011 |   0
   1100 |   1
   1101 |   X
   1110 |   1
   1111 |   0
   

3. (2 marks) Is x ∧ ¬ (¬ y ∨ x) is logically equivalent to x ∧ y? Prove your claim using a truth table. If it is not equivalent, identify values for x and y that demonstrate the inequivalence.
   
   
4. (2 marks) Convert each of the following base 10 representations to its equivalent binary form: use the fast method, and show your work. A solution that does not show intermediate values for the fast method will receive a mark of zero.
   
   131
   
   
5. (2 marks) Convert each of the following binary representations to its equivalent base 10 form: show your intermediate values.
   
   11.01101
   
   
6. (2 marks) Express the following values in binary notation: show your intermediate values.
   234
   
   
7. (2 marks) Perform the following additions in binary notation: show the carry bit, when appropriate.
   
   1011.11+10.01
   
   
8. (3 marks) Given the following:
   11011+11001
   the answer, and the interpretation of what the question is, will be different depending on whether binary or twos-complement representation is assumed. Report the decimal notation equivalent of the question, and the answer, of the sum under assumption of binary representation, and of twos-complement representation.
   
   
9. (2 marks) Convert the hex number ABC into decimal, by first converting to binary and then using the fast method -- show that you are using the fast method by giving the intermediate values (i.e., double or double plus one). A solution that does not show intermediate values for the fast method will receive a mark of zero.
   
   
10. (20 marks) Write a MARIE assembly language program that plays "guess the secret number", taking input from the user and responding "H" ("go Higher") or "L" ("go Lower") until the secret number is guessed. When it is guessed correctly, the program outputs the number, then outputs double the number, then outputs quadruple the number. Then the program halts. The program must utilize JnS-JumpI for the doubling subroutine. Use indenting of all code lines; only labels should appear completely left-justified.
    
    When your MARIE program is completed, email to gpruesse@otter.csci.viu.ca the code (the .mas file) as an attachment -- download the solution, calling it guess.mas (MARIE will attach the .mas extension); then attach that file to an email to the above address. You can do this on your own computer, using your own email service, or from the lab using the email service "pine". Send it with the subject "Assignment 1 Q 9". Only the MARIE code should be sent this way: the rest you should hand in on paper.