1

Chapter 2

Logic Functions and Gates

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Basic Logic Functions

The three basic logic functions are: AND OR NOT

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3

Logic Function Representation

Logic functions can be represented:algebraicallyusing truth tablesusing electronic circuits.

4

Algebraic Representation

Uses Boolean algebra. Boolean variables have two states

(binary). Boolean operatorsinclude

AND, OR, and NOT.

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5

Truth Table Representation

Defines the output of a function for every possible combination of inputs.

A system with n inputs has 2n possible combinations.

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Electronic Circuit Representation

Uses logic gates to perform Boolean algebraic functions.

Gates can be represented by schematic symbols.

Symbols can be either distinctive-shapeor rectangular-outline.

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7

Distinctive Shape Schematic Symbols

Uses different graphic representations for different logic functionsAND, OR, NOT.

Uses a bubble (a small circle) to indicate a logical inversion.

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Rectangular-Outline Schematic Symbols

All functions are shown in rectangular form with the logic function indicated by standard notation inside the rectangle.

The notation specifying the logic function is called the qualifying symbol.

Inversion is indicated by a 1/2 arrowhead.

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9

NOT Function

One input and one output. The output is the opposite logic level of

the input. The output is the complement of the

input.

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NOT Function Boolean Representation

Inversion is indicated by a bar over the signal to be inverted.

AY =

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11

NOT Function Electronic Circuit

Called a NOT gate or, more usually, an INVERTER.

Distinctive-shape symbol is a triangle with inversion bubble.

Rectangular-shape symbol uses 1 and the inversion 1/2 arrowhead.

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NOT Function Electronic Circuit

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13

AND Function

Two or more inputs, one output. Output is HIGH only when all of the

inputs are HIGH. Output is LOW whenever any input is

LOW.

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111001010000YBA

AND Function

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15

AND Boolean Representation

AND symbol is or nothing at all.

ABYB AY

==

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AND Function Electronic Circuit

Called an AND gate. Distinctive-shape symbol uses AND

designation. Rectangular-shape symbol use & as

designator.

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17

AND Function Electronic Circuit

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AND Function Electronic Circuit

10

19

0110000101010011

1

000A

111

001010000YCB

AND Function Electronic Circuit

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OR Function

Two or more inputs, one output. Output is HIGH whenever one or more

input is HIGH. Output is LOW only when all of the

inputs are LOW.

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21

OR Function

111

101

110

000

YBA

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OR Boolean Representation

OR symbol is +. Y = A + B

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23

OR Function Electronic Circuit

Called an OR gate. Distinctive-shape symbol uses OR

designation. Rectangular-shape symbol uses as

designator.

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OR Function Electronic Circuit

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25

Active Level

The logic level defined as ON for a circuit.

When a logic HIGH is ON, the signal is active-HIGH.

When a logic LOW is ON, the signal is active-LOW.

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NAND Function

Generated by inverting the output of the AND function.

Output is HIGH whenever any input is LOW.

Output is LOW only when all inputs are HIGH.

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27

NAND Function

011

101

110

100

YBA

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NAND Boolean Representation

Uses AND with an inversion overbar.

BAY =

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29

NAND Function Electronic Circuit

Called a NAND gate. Uses the AND symbol with inversion on.

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NAND Function Electronic Circuit

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31

NOR Function

Generated by inverting the output of the OR function.

Output is HIGH only when all inputs are LOW.

Outputs is LOW whenever any input is HIGH.

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011

001

010

100YBA

NOR Function

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33

NOR Boolean Representation

Uses OR with an inversion overbar.

BA Y +=

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NOR Function Electronic Circuit

Called a NOR gate. Uses OR symbol with inversion on the

output.

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NOR Function Electronic Circuit

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3 Input NOR and NAND FunctionTruth Tables

3 Input NAND:

3 Input NOR:

CBA Y =

C B A Y ++=

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01111111

0110000101010011

1

000A

011

001010100

CB C B A ++CBA

3 Input NOR and NAND FunctionTruth Tables

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Exclusive OR Gate

Two inputs, one output. Output is HIGH when one, and only one,

input is HIGH. Output is LOW when both inputs are

equal both HIGH or both LOW.

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39

Exclusive OR Gate

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011

101

110

000

YBA

Exclusive OR Gate

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41

Exclusive NOR Gate

Two inputs, one output. Output is HIGH when both inputs are

equal both HIGH or both LOW. Output is LOW when one, and only one,

input is HIGH, i.e., the two inputs are different.

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Exclusive NOR Gate

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111

001

010

100YBA

Exclusive NOR Gate

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Gate Equivalence NAND

A NAND gate can be represented by an AND gate with inverted output.

A NAND gate can be represented by an OR gate with inverted inputs.

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45

Gate Equivalence NAND

A

B

C

D

U1A

14011

1

23

U2A

14011

1

23

U3A

14011

1

23

Y

B

A

C

D

U4A

14071

1

23

U6A

14081

1

23

U7A

14081

1

23

Y

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Gate Equivalence NOR

A NOR gate can be represented by an OR gate with inverted output.

A NOR gate can be represented by an AND gate with inverted inputs.

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47

C

D

A

B U8A

14001

1

23

U9A

14001

1

23

U10A

14001

1

23

Y

C

D

B

A

U11A

14071

1

23

U12A

14071

1

23

U13A

14081

1

23 Y

Gate Equivalence NOR

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Gate Equivalence DeMorgan Forms

Change an AND function to an OR function and an OR function to an AND function.

Invert the inputs. Invert the outputs.

B

A

/B

/A

B

/A

A

/B

U14A

14011

1

23

U15A

14071

1

23

U18A

14001

1

23

U19A

14081

1

23

Y

Y

Y

Y

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DeMorgans Theorem - 1

Break the line and change the sign

B A BA +=B A BA =+

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DeMorgans Theorem - 2

The following are two common errors associated with DeMorgans Theorem:

B A BA ++

B A BA

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51

Active Logic Levels

Any INPUT or OUTPUT that has a BUBBLE is considered as active LOW.

Any INPUT or OUTPUT that has no BUBBLE is considered as active HIGH.

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Active Logic Levels - NOR

At least one input HIGH makes the

output LOW. All inputs LOW make the output HIGH.

BA Y +=

BA Y =

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Active Logic Levels - NOR

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Logic Switches

Provides a logic HIGH or LOW depending on switch position.

Commonly used types include normally-open pushbutton, normally-closed pushbutton, single-pole single-throw, and single-pole double-throw.

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55

Logic Switches

Open=>1Close=>0

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Logic Switches

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Two-Pole Push Button

Two-pole push button allows for normally HIGH and normally LOW levels from the same switch.

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Two-Pole Push Button

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Light Emitting Diodes (LEDs)

Used to indicate the status of a digital output.

Has two terminals the anode and the cathode.

If the anode is approximately 1.5 V greater than the cathode, current flows and the LED illuminates.

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Light Emitting Diodes (LEDs)

A C/K

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Light Emitting Diodes (LEDs)

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Light Emitting Diodes

Used to provide a visual indication of a logic state.

Can be wired to display active-HIGH or active-LOW.

Whats the common rated current flow through the diode? About 10mA

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Light Emitting Diodes

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Light Emitting Diodes

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Logic Gate Enable

The input to a gate that allows the output to respond to other inputs.

A logic LOW for an OR or NOR gate, a logic HIGH for an AND or NAND gate.

Somewhat like a controlled switch.

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VCC

VCCJump

CarrierDout Q11384

CB

E

D1

JP4HEADER 2

12

C3102/100V

R25

470

R224.7

U5B

4011

5

64

U5A

4011

1

23

R24SVR10K

13

2

R2610K

R212K

R231M

Control Input

DIP14 DIP14May be replaced by 3904.E B C1 2 3

Logic Gate Enable

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67

Logic Gate Inhibit

The input to a gate that forces the output to ignore any other input.

A logic HIGH for an OR or NOR gate, a logic LOW for an AND or NAND gate.

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Logic Gate Inhibit

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69

Logic Gate Inhibit

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Logic Gate Inhibit

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Logic Gate InhibitNote: P.51 Textbook Error; Forgot to add a inverter in the output terminal

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Logic Gate Inhibit

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Logic Gate Inhibit

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Y = 1

Y = B

OR

Y = 1

NAND

Y = 0

NOR

Y = B

XOR

A = 1

A = 0

Control

Y = BY = B

Y = 0

XNORAND

BY =

BY =BY =

B Y =

Logic Gate Inhibit

NAND, NOR, XNORAND, OR, NOR

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75

Tristate Buffer

Three output states, HIGH, LOW and high-impedance.

Requires a separate input to control which output state is selected.

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Tristate Buffer

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77

Tristate Buffer

Active Low!

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Tristate Buffer Utilization

Used to connect multiple outputs togetherAn action that requires highly attention!.

Used in controlling the operation of buses.

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79

Tristate Buffer Utilization

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The 74LS244 Octal Tri-State Buffer

Contains two groups of four non-inverting tri-state buffers.

Each group is controlled by a separate enable input, i.e., .G

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The 74LS244 Octal Tri-State Buffer

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Integrated Circuit Package

Integrated Circuits (ICs) contain many components in a single package.

Several packaging options are available. One common package is called dual-in-

line (DIP).

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83

Integrated Circuit Package

84

Integrated Circuit Technology

One common form is transistor-transistor logic, called TTL.

The other common form is Complementary Metal-Oxide Semiconductor, called CMOS.

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85

Low-voltage CMOS74LVX00

Advanced low-power Schottky TTL74ALS00FAST TTL74F00

Advanced BiCMOS (TTL/CMOS hybrid)74ABT00

High-speed CMOS (TTL-compatible inputs)74CT00High-speed CMOS74HC00

Low-power Schottky TTL74LS00Logic FamilyPart Number

Integrated Circuit Technology

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Integrated Circuit Designation

Standard form is 74XXFF, where 74 is the logic family identifier, XX is the logic family member and FF identifies the specific logic function.

SN74ALS00N

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87

IC Package Options

PLCC - plastic lead chip carrier SOIC - small outline integrated circuit TSSOP thin shrink small outline

package QFP quad flat pack DIP dual inline package BGA ball grid array

88

IC Package Options

SOICTSSOP

PLCC

DIP BGA

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89

PLCC 84 Pin Packages Can be mounted on the surface of a

circuit board or mounted in a socket. Pins are equally distributed on four sides. Pin 1 placed on the center of one of the

rows, as indicated by a dot. Pins number counterclockwise from this

point.

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PLCC 84 Pin Packages

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