I. Consider the following description of a Boolean function F1: the function F1 is true whenever (Y is True and Z is False) or (X is False and Z is True) or (X is False and Y is True); for all other cases F1 is False.
(a) Show the Boolean function representing F1
(b) Show the truth table of F1
a (c) Show a logic circuit diagram that implements F1 using AND, OR, and NOT gates.
II. (18 points: 6+6+6) Consider the Boolean function F2 = X ‘ . Z + X ‘ . Y . Z + X . Y ‘ + X . Y’ . Z
(a) Implement F2, in the form as given, using 2-input ANDs, 2-input ORs and NOT gates.
How many gates you used?
(b) Simplify F2 using Boolean algebra identities. Show all the steps & the identities used at each step.
(c) Implement the simplified form of F2 using 2-input ANDs, 2-input ORs and NOT gates.
How many gates you used now?
III. (16 points: 10 + 6) Consider the Boolean function F3 (A, B, C, D) = ( 0, 2, 4, 6, 12, 13, 14, 15 ).
(a) Find the minimum Sum Of Product form of F3 using the K-map method. Clearly show the groups on the K-Map.
(b) Assuming minterms 5 & 7 are Don’t Care conditions, redo the minimum SOP of F3.
Sample Solution
