Digital Fundamentals: A Systems
Approach
Thomas L. Floyd
Combinational Logic
Chapter 4
Ch.4 Summary
Combinational Logic Circuits
In Sum-of-Products (SOP) form, basic combinational
circuits can be directly implemented with AND-OR
combinations if the necessary complement terms are
available.
Digital Fundamentals: A Systems Approach
Thomas L. Floyd
© 2013 by Pearson Higher Education, Inc
Upper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.4 Summary
Combinational Logic Circuit Application
A storage tank monitor
Digital Fundamentals: A Systems Approach
Thomas L. Floyd
© 2013 by Pearson Higher Education, Inc
Upper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.4 Summary
AND-OR-Invert Logic
When the output of a SOP form is inverted, the circuit is
called an AND-OR-Invert circuit. The AOI configuration
lends itself to product-of-sums (POS) implementation.
The output from an AND-OR-Invert logic circuit is LOW
whenever A and B are HIGH, or C and D are HIGH.
Digital Fundamentals: A Systems Approach
Thomas L. Floyd
© 2013 by Pearson Higher Education, Inc
Upper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.4 Summary
Exclusive-OR Logic
The truth table for an exclusive-OR gate is
shown (right). Note that the output is HIGH
whenever A and B are unequal.
The Boolean expression is X = AB + AB
Digital Fundamentals: A Systems Approach
Thomas L. Floyd
© 2013 by Pearson Higher Education, Inc
Upper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.4 Summary
Exclusive-NOR Logic
The truth table for an exclusive-NOR gate is
shown (right). Note that the output is HIGH
whenever A and B are equal.
The Boolean expression is X = AB + AB
Digital Fundamentals: A Systems Approach
Thomas L. Floyd
© 2013 by Pearson Higher Education, Inc
Upper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.4 Summary
An Exclusive-NOR Logic Application
Data transmission with error detection
Digital Fundamentals: A Systems Approach
Thomas L. Floyd
© 2013 by Pearson Higher Education, Inc
Upper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.4 Summary
Implementing Combinational Logic
Implementing a SOP expression is done by first forming the
AND terms; then the terms are ORed together.
Digital Fundamentals: A Systems Approach
Thomas L. Floyd
© 2013 by Pearson Higher Education, Inc
Upper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.4 Summary
DeMorgan’s Theorem
The complement of two or more ANDed variables equals
the OR of the individual variable complements.
XY  X  Y
Digital Fundamentals: A Systems Approach
Thomas L. Floyd
© 2013 by Pearson Higher Education, Inc
Upper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.4 Summary
DeMorgan’s Theorem
The complement of two or more ORed variables equals
the AND of the individual variable complements.
X  Y  X Y
Digital Fundamentals: A Systems Approach
Thomas L. Floyd
© 2013 by Pearson Higher Education, Inc
Upper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.4 Summary
Universal Gates
NAND gates are
sometimes called
universal gates
because they
can be used to
produce the other
basic Boolean
functions.
Digital Fundamentals: A Systems Approach
Thomas L. Floyd
© 2013 by Pearson Higher Education, Inc
Upper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.4 Summary
Universal Gates
NOR gates are
also called
universal gates
because they can
be used to
produce the other
basic Boolean
functions.
Digital Fundamentals: A Systems Approach
Thomas L. Floyd
© 2013 by Pearson Higher Education, Inc
Upper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.4 Summary
Combinational Logic Application
Temperature control circuit block diagram
Digital Fundamentals: A Systems Approach
Thomas L. Floyd
© 2013 by Pearson Higher Education, Inc
Upper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.4 Summary
Combinational Logic Application
Temperature
control logic
implementation
Digital Fundamentals: A Systems Approach
Thomas L. Floyd
© 2013 by Pearson Higher Education, Inc
Upper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.4 Summary
Key Terms
Universal
gate
Either a NAND or a NOR gate. The term
universal refers to a property of a gate that
permits any logic function to be implemented
by that gate or by a combination of gates of
that kind.
Negative-OR
The dual operation of a NAND gate when the
inputs are active-LOW.
Negative-AND The dual operation of a NOR gate when the
inputs are active-LOW.
Digital Fundamentals: A Systems Approach
Thomas L. Floyd
© 2013 by Pearson Higher Education, Inc
Upper Saddle River, New Jersey 07458 • All Rights Reserved