E1.2 Digital Electronics 1
5.1
31 October 2008
Lecture 5: Logic Simplification &
Karnaugh Maps
Dr Pete Sedcole
Department of E&E Engineering
Imperial College London
http://cas.ee.ic.ac.uk/~nps/
(Floyd 4.5 – 4.10)
(Tocci 4.1 – 4.5)
E1.2 Digital Electronics 1
5.2
31 October 2008
In this lecture:
•
Standard form of Boolean Expression:
– Sum-of-Products & Product-of-Sums (SOP/POS)
– Canonical form
•
Boolean simplification with Boolean algebra
•
Boolean simplification with Karnaugh Maps
•
The “Don’t care” logic state
E1.2 Digital Electronics 1
5.3
31 October 2008
Forms of Boolean Expressions
•
Sum-of-products (SOP)
– e.g.: X = ABC + DEF + AEF
– the product (AND) terms are formed first, then
summed (OR)
•
Product-of-sums (POS)
– e.g.: Y = (A+B+E)(C+D+E)(B+F)
– the sum (OR) terms are formed first, then the product
(AND)
•
It is possible to convert between the two forms using
DeMorgan’s theorems.
E1.2 Digital Electronics 1
5.4
31 October 2008
Canonical form
•
In the canonical form of a Boolean expression, every
variable appears in every term
– e.g.:
•
Canonical form is not an efficient way of writing the
Boolean expression, but is useful sometimes in
design and analysis
D
C
B
A
CD
B
A
D
C
AB
D
C
B
A
f
+
+
=
)
,
,
,
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