1
PHYS 331: Junior Physics Laboratory I
Notes on Digital Circuits
Digital circuits are collections of devices that perform logical operations on two logical
states, represented by voltage levels. Standard operations such as AND, OR, INVERT,
EQUIVALENT, etc. are performed by devices known as gates. Groups of compatible gates can
be combined to make yes/no decisions based on the states of the inputs. For example, a simple
warning light circuit might check several switch settings and produce a single yes/no output.
More complicated circuits can be used to manipulate information in the form of decimal digits,
alphanumeric characters, or groups of yes/no inputs. These notes are intended to familiarize you
with the elementary principles of this field.
A. Analysis of asynchronous logic
Suppose we have a statement which can be true or false, perhaps representing the
presence or absence of a particle, a light signal on or off, a voltage present or absent, or any other
binary possibility. For now we will ignore the physical meaning of the statement and ask how
one would decide the logical truth or falsehood of combinations of such statements, a subject
called combinatoric logic. If we denote the "truth value" of a statement
A
by 0 or 1, the standard
combinations are shown in the form of "truth tables" in Fig. 1. These basic combinations, or
A
B
Q
0
0
0
0
1
0
1
0
0
1
1
1
AND
A
B
Q
A
B
Q
0
0
0
0
1
1
1
0
1
1
1
1
OR
A
B
Q
A
A
Q
0
1
1
0
NOT
A
B
Q
0
0
1
0
1
1
1
0
1
1
1
0
NAND
A
B
Q
A
B
Q
0
0
1
0
1
0
1
0
0
1
1
0
NOR
A
B
Q
A
B
Q
0
0
0
0
1
1
1
0
1
1
1
0
XOR
A
B
Q
Q
Fig. 1 Standard logic symbols and truth tables.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document2
similar ones, have been implemented in electronic circuitry, where truth values can be
represented by different voltage levels. The standard circuit symbols are also shown in Fig. 1.
By combining the basic operations we can construct other logical functions. For example,
suppose we wish to determine whether or not a particle has stopped in a target, using the
configuration of counters shown in Fig. 2. A particle passing through a counter makes the
corresponding output true, and we assume the particle has stopped in the target if
A
and
B
are
both true, but
C
is false. Formally, we want to know when the compound statement
A
•
B
•
C
is
true. An electronic implementation of the compound statement is also shown in Fig. 2, together
with a truth table. Examination of the truth table shows that
A
•
B
•
C
is true in exactly one
situation, which corresponds to the physically desired result.
Sometimes it is not obvious how to write down the required expression and implement it.
You might discover an implementation using only standard operations by trial and error, but it is
possible to be more systematic. For example, suppose we wish to make an exclusiveOR
function using AND, OR and NOT gates. To do this we can try to combine some statements that
are true for exactly one combination of
A
and
B
. Consider the following:
A
•
B
is true only when
A
= 1 and
B
= 1
A
•
B
is true only when
A
= 1 and
B
= 0
(1)
A
•
B
is true only when
A
= 0 and
B
= 1
A
•
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 Volt, Boolean Algebra, Logic gate, Logical connective, Propositional calculus

Click to edit the document details