CS 14 -- Problem set 1

Combinational and Sequential Logic Circuits

Answer the questions below clearly and completely. This assignment is due Monday, February 14^th at 10:00 am.

1. Use Karnaugh maps to simplify the logic functions described by the truth table below. You do not need to draw the corresponding circuit -- a boolean algebraic expression for the output is sufficient.

   a.
   	A   B   C   Output
   	------------------
   	0   0   0        1
   	0   0   1        1
   	0   1   0        0
   	0   1   1        0
   	1   0   0        1
   	1   0   1        1
   	1   1   0        0
   	1   1   1        1
   
   b.
   	A   B   C   D   Output
   	----------------------
   	0   0   0   0        1
   	0   0   0   1        1
   	0   0   1   0        1
   	0   0   1   1        0
   	0   1   0   0        0
   	0   1   0   1        0
   	0   1   1   0        1
   	0   1   1   1        0
   	1   0   0   0        1
   	1   0   0   1        1
   	1   0   1   0        1
   	1   0   1   1        0
   	1   1   0   0        1
   	1   1   0   1        1
   	1   1   1   0        0
   	1   1   1   1        1
   	

2. Convert the following formula from sum-of-products to product-of-sums form:

         _ _       _ _
     Y = A B C + A B C
   	

3. Design a sequential logic circuit that emits the following, repeating pattern that has a period (a repetition length) of 7:

   0 1 1 0 0 1 1 ...

   (Hint 1: Your counter, as designed in lab, is a clocked circuit that emits a repeating pattern. Hint 2: Just because you're using a counter doesn't mean that its raw value is what needs to be emitted.)

4. Using only algebraic manipulation, show that the following two boolean expressions are equivalent:

     _    _
     AB + AC
     _    __
     AB + ABC