tut07.pdf - Mat1101 Tutorial 7 Karnaugh Maps, Digital...

Mat1101 Tutorial 7
Karnaugh Maps, Digital Circuits and Boolean Notation
Grossman Chapter 8
1. The following logical statements have been written using the boolean short hand.
Write the equivalent statements using ∧, ∨, and ¬ . Using the laws of logic simplify the
following, where possible.
(a) ?(? + ?
′
?)
(b) (??
′
+ ?
′
)
′
2. For the logical statements in Question 1, complete the following:
(a) Draw the digital circuit corresponding to the original expression.
(b) Construct a truth table and hence, find the disjunctive normal form of the ex-
pression.
(c) Use a Karnaugh Map to simplify the statements. Verify your simplification using
a truth table.
3. Write the boolean expression (?
′
+ ?)(??)
′
in disjunctive normal form.
4. Consider the following Boolean expression:
??
′
?
′
+ ?
′
?? + ?
′
?
′
? + ?
′
??
′
+ ?
′
?
′
?
′
.
Use the Karnaugh map below to simplify the expression.