Digital Fundamentals

Functions of

combinational logic

Objectives

•Distinguish between half-adders and full-adders

•Use full-adders to implement multibit parallel binary adders

•Explain the differences between ripple carry and look-ahead carry parallel adders

•Use the magnitude comparator to determine the relationship between two binary numbers and use cascaded comparators to handle the comparison of larger numbers

•Implement a basic binary decoder

•Use BCD-to-7-segment decoders in display systems

•Apply a decimal-to-BCD priority encoder in a simple keyboard application

•Convert from binary to Gray code, and Gray code to binary by using logic devices

Functions of Combinational Logic 2

•Convert from binary to Gray code, and Gray code to binary by using logic devices

•Apply multiplexers in data selection, multiplexed displays, logic function generation, and simple communications systems

•Use decoders as demultiplexers

•Explain the meaning of parity

•Use parity generators and checkers to detect bit errors in digital systems

•Implement a simple data communications system

•Identify glitches, common bugs in digital systems

•Describe basically how SPLDs are programmed

Half-adder

Functions of Combinational Logic 3

Full-adder

Functions of Combinational Logic 4

Full-adder implementation with half-adders

Functions of Combinational Logic 5

Functions of Combinational Logic 6

Parallel binary adders

Functions of Combinational Logic 7

Functions of Combinational Logic 8

Functions of Combinational Logic 9

Four-bit parallel adders

Functions of Combinational Logic 10

Examples of 4-bit paralleladders in the IC form

Functions of Combinational Logic 11Specs for the 74LS283

Adder expansion

Functions of Combinational Logic 12

Functions of Combinational Logic 13

Application example – voting system

Functions of Combinational Logic 14

Comparators -equality

Functions of Combinational Logic 15

Functions of Combinational Logic 16

Inequality

Example 6-6Determine the states of the three outputs withthe following inputs:

Functions of Combinational Logic 17

Solution: A=0110, B=0011. A>B is HIGH,and others outputs LOW.

A 4-bit magnitude comparator – 74HC85

Functions of Combinational Logic 18

Example 6-7Use 74HC85 comparators to compare the magnitudes of two 8-bit numbers. Show the comparators withproper interconnections.

Solution:

Functions of Combinational Logic 19

Functions of Combinational Logic 20

Decoders – basic binary decoder

Functions of Combinational Logic 21

determines if input=1001 and sets the output to HIGH level

accordingly

Functions of Combinational Logic 22

4-bit decoder

Decoding functions and the truth table for a 4-line-to-16-line (1-of-16) decoder with active-LOW outputs

Functions of Combinational Logic 23

Logic symbol for 4-line-to-16-linedecoder

Functions of Combinational Logic 24

74HC154 IC decoder

Functions of Combinational Logic 25

Functions of Combinational Logic 26

Application example

Functions of Combinational Logic 27

BCD-to-decimal decoder

Functions of Combinational Logic 28

Functions of Combinational Logic 29

BCD-to-7-segment decoder

Functions of Combinational Logic 30

74LS47 BCD-to-7-segment decoder/driver

Functions of Combinational Logic 31

Functions of Combinational Logic 32

Encoders – decimal-to-BCD encoder

Functions of Combinational Logic 33

74HC147 decimal-to-BCD priority encoderHPRI means highest value input has priority

Functions of Combinational Logic 34

74F148 8-line-to-3-line encoder

Functions of Combinational Logic 35

16-line-to-4-line encoder using a couple of 74F148 ICs and external logic

Functions of Combinational Logic 36

Functions of Combinational Logic 37

Application example – keyboard encoder

Functions of Combinational Logic 38

Code converters – BCD-to-binary conversion

Functions of Combinational Logic 39

Functions of Combinational Logic 40

Binary-to-Gray conversion

Gray-to-binary conversion

Functions of Combinational Logic 41

Binary-to-Gray conversion

Functions of Combinational Logic 42

Multiplexers (data selectors)

Functions of Combinational Logic 43

1-of-4 data selector/multiplexer

Functions of Combinational Logic 44

74HC157A quaruple 2-input data selector/multiplexer

Functions of Combinational Logic 45

74LS151 8-input data selector/multiplexer

Functions of Combinational Logic 46

Functions of Combinational Logic 47

Application example – 7-segment displaymultiplexer

Functions of Combinational Logic 48

Functions of Combinational Logic 49

Functions of Combinational Logic 50

Functions of Combinational Logic 51

Demultiplexers

1-line-to-4-line demultiplexer

Functions of Combinational Logic 52

Functions of Combinational Logic 53

74HC164 decoder used as ademultiplexer

Functions of Combinational Logic 54

Parity generators/checkers

Basic parity logic

Functions of Combinational Logic 55

74LS280 9-bit parity generator/checker

Functions of Combinational Logic 56

Data transmission system witherror detection

Functions of Combinational Logic 57

Troubleshooting - glitch

Functions of Combinational Logic 58

Functions of Combinational Logic 59

Elimination of glitches with strobing

THINK! How does it work?

Functions of Combinational Logic 60

Functions of Combinational Logic 61

Programmable logic

Functions of Combinational Logic 62

•Computer•software•programmer

SPLD conventional programming sequence

Functions of Combinational Logic 63

Functions of Combinational Logic 64

ISP – in system programmable SPLDs

JTAG

Functions of Combinational Logic 65

Functions of Combinational Logic 66

Functions of Combinational Logic 67

How this can be done?

Functions of Combinational Logic 68

Ts

Functions of Combinational Logic 69

State diagram

Functions of Combinational Logic 70

Functions of Combinational Logic 71

Functions of Combinational Logic 72

Summary

Functions of Combinational Logic 73

IC types

Functions of Combinational Logic 74

Functions of Combinational Logic 75