1

Chapter 6

Functions of Combinational Logic

2

Figure 6--1 Logic symbol for a half-adder

Adder

3

4

Figure 6--2 Half-adder logic diagram.

5

Figure 6--3 Logic symbol for a full-adder

6

7

Figure 6--4 Full-adder logic

8

Figure 6--5 Full-adder implemented with half-adders.

9

Figure 6--7 Block diagram of a basic 2-bit parallel adder using two full-adders.

10

Figure 6--9 A 4-bit parallel adder.

11

Figure 6--10 Four-bit parallel adders.

12

Figure 6--12 Examples of adder expansion.

13

Figure 6--13 Two 74LS83A adders connected as an 8-bit parallel adder (pin numbers are in parentheses).

14

Figure 6--14 A voting system using full-adders and parallel binary adders.

15

Figure 6--15 Basic comparator operation. (Equality)

Comparators

16

Figure 6--16 Logic diagram for equality comparison of two 2-bit numbers

17

Figure 6--17 : Example 6-5

18

Figure 6--18 Logic symbol for a 4-bit comparator with inequality indication.

19

Figure 6—19 : Example 6-6

20

Figure 6--20 Pin diagram and logic symbol for the 74HC85 4-bit magnitude comparator (pin numbers are in parentheses).

21

Figure 6--21 An 8-bit magnitude comparator using two 74HC85s.

22

Figure 6--22 Decoding logic for the binary code 1001 with an active-HIGH output.

Decoders

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Figure 6--23 Decoding logic for producing a HIGH output when 1011 is on the inputs.

24Figure 6--24 Logic symbol for a 4-line-to-16-line (1-of-16) decoder.

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26

Figure 6--28 The 74HC42 BCD-to-decimal decoder.

BCD-to-Decimal Decoder

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28Figure 6--29

29

Figure 6--30 Logic symbol for a BCD-to-7-segment decoder/driver with active-LOW outputs.

BCD-to-7-Segment Decoder

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Figure 6--31 Pin diagram and logic symbol for the 74LS47 BCD-to-7-segment decoder/driver.

31Figure 6--32 Examples of zero suppression using the 74LS47 BCD to 7-segment decoder/driver.

32

Figure 6--33 Logic symbol for a decimal-to-BCD encoder.

Encoders

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Figure 6--34 Basic logic diagram of a decimal-to-BCD encoder. A 0-digit input is not needed because the BCD outputs are all LOW when there are no HIGH inputs.

34

Figure 6--35 Pin diagram and logic symbol for the 74HC147 decimal-to-BCD priority encoder (HPRI means highest value input has priority).

35

Figure 6--36 Logic symbol for the 74F148 8-line-to-3-line encoder.

36

Figure 6--37 A 16-line-to-4 line encoder using 74F148s and external logic.

37Figure 6--38 A simplified keyboard encoder.

38

Code Converter

BCD-to-Binary Conversion

39

Figure 6--39 Four-bit binary-to-Gray conversion logic.

40

Figure 6--40 Four-bit Gray-to-binary conversion logic

41

Figure 6--41 : Example 6-13

42

Figure 6--42 Logic symbol for a 1-of-4 data selector/multiplexer.

Multiplexers (Data Selectors)

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44

Figure 6--43 Logic diagram for a 4-input multiplexer.

45

Figure 6--44

46

Figure 6--45 Pin diagram and logic symbol for the 74HC157A quadruple 2-input data selector/multiplexer.

47

Figure 6--46 Pin diagram and logic symbol for the 74LS151 8-input data selector/multiplexer.

48

Figure 6--47 A 16-input multiplexer.

49Figure 6--48 Simplified 7-segment display multiplexing logic.

50

Figure 6--51 A 1-line-to-4-line demultiplexer.

Demultiplexers

51Figure 6--52

52Figure 6--53 The 74HC154 decoder used as a demultiplexer.

53

Figure 6--54

Parity Generators/Checkers

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Figure 6--55 The 74LS280 9-bit parity generator/checker.

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Figure 6--61 Typical configuration for conventional PLD programming.

Programmable Logic

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Figure 6--62 Flow chart of an SPLD conventional programming sequence.

57

Figure 6--63 Typical configuration for in-system programming of a PLD.