Dld-chap - 3-logic Gates 6v5o9

Digital Logic Design Chapter 3 Logic Gates

Logic Gates 

Inverter



AND Gate



OR Gate



Exclusive-OR Gate



NAND Gate



NOR Gate



Exclusive-NOR Gate

Floyd Digital Fundamentals, 9/e

Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

Slide 2

The Inverter



Slide 3

The Inverter 

The inverter performs the Boolean

NOT operation. When the input is LOW, the output is HIGH; when the input is HIGH, the output is LOW.

Pulsed waveforms Truth table 0 = LOW 1 = HIGH

Boolean expression

The output of an inverter is always the complement (opposite) of the input.



Slide 4

The AND Gate



Slide 5

The AND Gate 

The AND gate produces a HIGH output when all inputs are HIGH; otherwise, the output is LOW.



Slide 6

The AND Gate The AND operation is usually shown with a dot between the variables but it may be implied (no dot). Thus, the AND operation is written as X = A .B or X = AB.

Boolean expression Truth table 0 = LOW 1 = HIGH

Pulsed waveforms

The output of an AND gate is HIGH only when all inputs are HIGH.



Slide 7

The AND Gate

3-Input AND Gate

4-Input AND Gate



Slide 8

The AND Gate The AND operation is used in computer programming as a selective mask  If you want to retain certain bits of a binary number but reset the other bits to 0, you could set a mask with 1’s in the position of the retained bits. Example: If the binary number 10100011 is ANDed with the mask 00001111, what is the result? 00000011 



Slide 9

The AND Gate 

A common application of the AND gate is to enable (that is, to allow) the age of a signal (pulse waveform) from one point to another at certain times and to inhibit (prevent) the age at other times.



Slide 10

The OR Gate



Slide 11

The OR Gate 

The OR gate produces a HIGH output if any input is HIGH; if all inputs are LOW, the output is LOW.



The OR operation is shown with a plus sign (+) between the variables. Thus, the OR operation is written as X = A + B



Slide 12

The OR Gate


Pulsed waveforms

The output of an OR gate is HIGH whenever one or more inputs are HIGH Floyd Digital Fundamentals, 9/e


Slide 13

The OR Gate

3-Input OR Gate

4-Input OR Gate



Slide 14

The OR Gate 

The OR operation can be used in computer programming to set certain bits of a binary number to 1. Example: ASCII letters have a 1 in the bit 5 position for lower case letters and a 0 in this position for capitals. (Bit positions are numbered from right to left starting with 0.) What will be the result if you OR an ASCII letter with the 8-bit mask 00100000? The resulting letter will be lower case



Slide 15

The OR Gate



Slide 16

The NAND Gate



Slide 17

The NAND Gate 

The NAND gate produces a LOW output when all inputs are HIGH; otherwise, the output is HIGH.



Slide 18

The NAND Gate


Pulsed waveforms

The output of a NAND gate is HIGH whenever one or more inputs are LOW. Floyd Digital Fundamentals, 9/e


Slide 19

The NAND Gate

3-Input NAND Gate

4-Input NAND Gate

The NAND gate is particularly useful because it is a “universal” gate – all other basic gates can be constructed from NAND gates.



Slide 20

The NOR Gate



Slide 21

The NOR Gate 

The NOR gate produces a LOW output if any input is HIGH; if all inputs are HIGH, the output is LOW.



Slide 22

The NOR Gate


Pulsed waveforms

The output of a NOR gate is LOW whenever one or more inputs are HIGH. Floyd Digital Fundamentals, 9/e


Slide 23

The NOR Gate

3-Input NOR Gate

4-Input NOR Gate



Slide 24

Exclusive-OR and Exclusive-NOR Gates



Slide 25

Exclusive-OR Gate 

The XOR gate produces a HIGH output only when both inputs are at opposite logic levels.



Slide 26

Exclusive-OR Gate


Pulsed waveforms

The output of an XOR gate is HIGH whenever the two inputs are different. Floyd Digital Fundamentals, 9/e


Slide 27

Exclusive-OR Gate Question: If the A and B waveforms are both inverted for the above waveforms, how is the output affected?



There is no change in the output.



Slide 28

Exclusive-NOR Gate The XNOR gate produces a HIGH output only when both inputs are at the same logic level.


Pulsed waveforms

The output of an XNOR gate is HIGH whenever the two inputs are identical. Floyd Digital Fundamentals, 9/e


Slide 29

Exclusive-NOR Gate 

Notice that the XNOR gate will produce a HIGH when both inputs are the same. This makes it useful for comparison functions.

Question: If

the A waveform is inverted but B remains the same, how is the output affected?  The output will be inverted. Floyd Digital Fundamentals, 9/e


Slide 30

Recommended Readings 

Example 3-13



Example 3-18



Slide 31

Fixed-Function Logic



Slide 32

Fixed Function Logic



Slide 33




Slide 34




Slide 35




Slide 36

Programmable Logic



Slide 37

Programmable Logic 

A Programmable Logic Device (PLD) can be programmed to implement logic. There are various technologies available for PLDs. Many use an internal array of AND gates to form logic . Many PLDs can be programmed multiple times.



Slide 38

Programmable Logic



Slide 39

Programmable Logic



Slide 40

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