x
y
F=x
OR
y
F=x
NOR
y
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
Figure 6.3 Truth table for OR and NOR gates
c.
AND & NAND Gates
AND
gate takes two or more inputs and produces an output of
1
if and only if all the
inputs are
1
, otherwise it gives
0
outputs. On the other hand,
NAND
gate produces an
output of
0
for only when all the inputs are
1
.
The logic symbol for twoinput AND & NAND gates is drawn in fig. 6.4.
x
y
F
x
y
F
(a) AND Gate Symbol
(b) NAND Gate Symbo
Figure 6.4 Logic symbols for OR & NOR gates
Truth table for AND & NAND Gate is shown in the table below
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Electrical Engineering
x
y
F=x
AND
y
F=x
NAND
y
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
Figure 6.5 Truth table for AND & NAND gate
d.
XOR and XNOR Gates
XOR
(exclusive OR) logic gate is a special class of derived logic gate that produce an
output of
1
, only when one of the inputs is
1
.
XNOR
does the opposite of
XOR
which
outputs
0
when one of the inputs is
1.
The logic symbol for XOR and XNOR gates is shown in figure 6.6.
X
Y
X
Y
(a) XOR gate
(b) XNOR gate
F
F
Figure 6.6 Logic symbol for XOR and XNOR gates
Truth table of XOR and XNOR gates for two inputs is given in the following table.
x
y
F=x
XOR
y
F=x
XNOR
y
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
Figure 6.7 Truth table of twoinput XOR and XNOR gates
6.2 REALIZATION OF DISCREET LOGIC GATES
Visualization of Gates with Binary switches
Two binary switches can be connected together either in series or in parallel to develop AND &
OR gate operations respectively.
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Electrical Engineering
+

X
Y
F
R
+5V
+

X
Y
F
R
+5V
(a)
(b)
.
Figure 6.8 Switch realizations of gates
If two switches are connected in series as in figure 6.8 (a), then both switches have to be
on
in
order for the output
F
to be a
1
. In other words,
F
= 1 if
x
= 1 and
y
= 1. If either
x
or
y
is off,
or both are off, then
F
= 0. This can be translated into the
AND
gate operation.
If we connect two switches in parallel as in figure 6.8 (b), then only one switch needs to be
on
in order for the output F to be a
1
. In other words, F = 1 if either x = 1, or y = 1, or both x and
y are 1’s. This means that F = 0 only if both x and y are
0
’s. This is similar to the operation of
OR
gate.
Realization of Gates with Digital Integrated Circuit
Physical circuits deal with physical properties, such as voltages and currents. Digital circuits
use the abstractions of
0
and
1
to represent the presence or absence of these physical properties.
In fact, a range of voltages is interpreted as the
logic 0
, and another, nonoverlapping range is
interpreted as the
logic 1
. These ranges vary for different logic families. Traditionally, digital
circuits operate with a 5volt power supply. In such a case, it is customary to interpret the
voltages in the range 0– 1.5 V as
logic 0
, while voltages in the range 3.5–5 V as
logic 1
. This
is shown in Figure 6.9. Voltages in the middle range (from 1.5–3.5 V) are undefined and should
not occur in the circuit except during transitions from one state to the other. However, they
may be interpreted as a “weak” logic 0 or a “weak” logic 1.
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 Fall '19
 Logic gate