Chapter 3 (part 2)
Basic Logic Gates
1 1
3-7 The Inverter
• Used to complement (invert) a digital signal
– When A = 1, X = 0
– When A = 0, X = 1
• Timing analysis
2
Truth table and Boolean equations
for the Inverter
• Truth Table
• Boolean Equation:
X=A
• Inversion bar
– Used to signify the
complement
• Inverter is also called
as NOT gate
3
3-8 The NAND Gate
• Same as the AND gate except that its output
is inverted
– If A = 1 and B = 1, X = 0
– If A = 0 or B = 0, A = 1
4
I/O of a 7400 quad NAND IC
5
Truth table and Boolean equations for
the NAND Gate
• Boolean Equation: X = AB
• Multiple inputs - the output is always HIGH
unless all inputs go HIGH
6
Symbols for three- and eight-input
NAND gates
7
8
9
10
3-9 The NOR Gate
• Same as the OR gate except that its output
is inverted
– If A = 1 or B = 1, X = 0
– If A = 0 and B = 0, X = 1
11
I/O of a 7402 quad NOR IC
12
Truth Table and Boolean equation
for The NOR Gate
• Truth Table
• Boolean Equation: X = A + B
13
14
15
16
3-10 Logic Gate Waveform Generation
A popular general
Purpose Repetitive
waveform generator
17
Figure 3.44 Generating a 3-ms HIGH pulse
using an AND gate and a Johnson shift
counter.
18
Example 3-13 Which Johnson counter outputs
will you connect to an AND gate to get a 1ms
HIGH-level output from 4 to 5ms?
19
Example 3-14 Which Johnson counter outputs
must be connect to a three-input AND gate to
enable just the Cp#4 pulse only to be output?
20
Example 3-15 Sketch the output waveform
resulting from inputting the Johnson counter
outputs shown:
21
22
23
24
25
Figure 3.60 7404 TTL and 4049 CMOS
inverter pin configurations.
26
Figure 3.61 (a) 7402
TTL NOR and 4001
CMOS NOR pin
configurations;
(b) 7400 TTL NAND and
4011 CMOS NAND pin
configurations.
27
28
3-12 IEEE/IEC Standard Logic
Symbols
29
30
Summary
• The AND gate requires that all inputs are
HIGH in order to get a HIGH output.
• The OR gate outputs a HIGH if any of its
inputs are HIGH.
• An effective way to measure the precise
timing relationships of digital waveforms is
with an oscilloscope or a logic analyzer.
31
Summary
• Beside providing the basic logic functions,
AND and OR gates can also be used to
enable or disable a signal to pass from one
point to another.
• There are several integrated circuits available
in both TTL and CMOS that provide the basic
logic functions.
32
Summary
• Two important troubleshooting tools are the
logic pulser and the logic probe. The pulser
is used to inject pulses into a circuit under
test. The probe reads the level at a point in a
circuit to determine is it is HIGH, LOW, or
floating.
• An inverter provides an output that is the
complement of its input.
33
Summary
• A NAND gate outputs a LOW when all of its
inputs are HIGH.
• A NOR gate outputs a HIGH when all of its
inputs are LOW.
• Specialized waveforms can be created by
using a repetitive waveform generator and
the basic gates.
34 40