Department of Electrical and Computer Engineering
North Carolina State University

ECE 212 FALL, 1994

EXAM 1 - A Solution
September 27, 1994

Instructions: This is an open book exam but you are not permitted to use notes or a calculator. Put everything away except your pencil or pen and your book. Do all work on the test provided. If you need extra paper, raise your hand and extra paper will be provided. However, you should be able to do all of your work on the test itself. A space has been provide for each answer. Make sure that you put your answers in these spaces. Also, put your name on each page in the space provided for this purpose.

 Name:             Solution

                 Student Number:

1. (Truth Tables) An increment by 4 function takes a 3 bit number as input and generates an output corresponding to adding 4 to the input number. For example, if the input is 011 (representing 3) then the output will be 0111 (representing 7).

    a.  

   Complete the truth table given in Table 1 for this function.

    
   Table 1: Truth Table for Problem 1.
   

    b.  

   Represent the output functions in product of sums form using the ``big M'' notation.

2. (Boolean Function Minimization) Consider the Boolean function

   Use a Karnaugh Map to find a minimized product of sums expression for F(A,B,C,D)

    a.  

   Groups of 4: (2,3,6,7), (6,7,14,15), (2,6,10,14)

    b.  

   Groups of 2: (5,7)

    c.  

   Single minterms: 9

   All are required because requires (2,3,6,7), requires (6,7,14,15), requires (2,6,10,14), requires (5,7) and is a single maxterm. Thus,

3. (Canonical Forms) A Boolean expression for the function F(A,B,C,D) is given by

    a.  

   Use DeMorgan's theorem to compute the complement of F(A,B,C,D).

    b.  

   Write F(A,B,C,D) as a Boolean expression in canonical maxterm form.

    c.  

   Write F(A,B,C,D) as a product of sums using ``big M'' notation.

    d.  

   Write using ``little m'' notation.

4. (Boolean Function Minimization) Use a Karnaugh map to find a minimum sum of products expression for the following function

    a.  

   Groups of 4: (0,8,16,24), (0,4,16,20), (4,5,20,21), (16,20,24,28), (16,18,24,26)

    b.  

   Groups of 2: (3,11), (23,31), (27,31)

    c.  

   Single minterms: 14

   We now need to find a minimum cover of the minterms. requires (4,5,20,21). This takes care of , and . requires group (16,18,24,26). This takes care of and . requires (3,11). This takes care of . is required as a single minterm. We can use either (0,8,16,24) or (0,4,16,20) to cover and we can use either (23,31) or (27,31) to cover . Choosing (0,8,16,24) and (23,31), we have

   Choosing (0,4,16,20) and (27,31), we have

   The other combinations are also valid.

5. (Addition/Subtraction in Different Bases) Perform the indicated arithmetic operations.

    a.  

   in base 7

    b.  

   in base 5

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