Answer the questions below clearly and completely. This assignment is due Monday, February 14th at 10:00 am.
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
_ _ _ _ Y = A B C + A B C
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.)
Using only algebraic manipulation, show that the following two boolean expressions are equivalent:
_ _ AB + AC _ __ AB + ABC