1. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 1 Digital Fundamentals CHAPTER 6 Functions of Combinational Logic

2. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 2 Basic Adders

3. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 3 Half-Adder 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 10 Zero plus zero equals zero Zero plus one equals one One plus zero equals one One plus one equals zero with a carry of one Simple Binary Addition

4. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 4 Half-Adder

5. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 5 Full-Adder

6. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 6 Full-Adder Full adder from two half-adder circuitsFull adder from two half-adder circuits

7. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 7 Parallel Binary Adders Parallel Binary Adders

8. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 8 Parallel Binary Adders Two-bit parallel binary adderTwo-bit parallel binary adder

9. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 9 Parallel Binary Adders Four-bit parallel binary adderFour-bit parallel binary adder

10. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 10 Comparators 1-Bit Comparator1-Bit Comparator 2-Bit Comparator2-Bit Comparator 4-Bit Comparator4-Bit Comparator

11. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 11 Comparators 1-Bit Comparator1-Bit Comparator The output is 1 when the inputs are equal

12. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 12 Comparators 2-Bit Comparator2-Bit Comparator The output is 1 when A 0 = B 0 AND A 1 = B 1

13. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 13 Comparators 4-Bit Comparator4-Bit Comparator One of three outputs will be HIGH: A greater than B (A > B)A greater than B (A > B) A equal to B (A = B)A equal to B (A = B) A less than B (A < B)A less than B (A < B)

14. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 14 Decoders

15. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 15 Decoders Binary decoderBinary decoder 4-bit decoder4-bit decoder BCD-to-decimal decoderBCD-to-decimal decoder BCD-to-7-segement decoderBCD-to-7-segement decoder

16. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 16 Decoders Binary decoderBinary decoder The output is 1 only when: A 0 = 1 A 2 = 0 A 3 = 0 A 4 = 1 This is only one of an infinite number of examples

17. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 17 Decoders 4-bit decoder4-bit decoder Logic Diagram

18. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 18 Decoders 4-bit decoder4-bit decoder –Binary inputs –Active-low outputs Truth Table

19. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 19 Decoders BCD-to-decimal decoderBCD-to-decimal decoder

20. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 20 Decoders BCD-to-7-segement decoderBCD-to-7-segement decoder Logic Diagram

21. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 21 Decoders BCD-to-7-segement decoderBCD-to-7-segement decoder Truth Table

22. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 22 Encoders

23. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 23 Encoders Decimal-to-BCD encoderDecimal-to-BCD encoder 8-line-to-3-line encoder8-line-to-3-line encoder

24. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 24 Encoders Decimal-to-BCD encoderDecimal-to-BCD encoder

25. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 25 Encoders 8-line-to-3-line encoder8-line-to-3-line encoder

26. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 26 Code Converters

27. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 27 Code Converters BCD-to-binary conversionBCD-to-binary conversion Binary-Gray conversionsBinary-Gray conversions

28. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 28 Code Converters BCD-to-binary conversionBCD-to-binary conversion

29. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 29 Code Converters Binary-Gray conversionsBinary-Gray conversions

30. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 30 Multiplexers (Data Selectors)

31. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 31 Multiplexers (Data Selectors) 4-input multiplexer4-input multiplexer Expanded multiplexersExpanded multiplexers

32. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 32 Multiplexers (Data Selectors) 4-input multiplexer4-input multiplexer

33. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 33 Multiplexers (Data Selectors) Expanded multiplexersExpanded multiplexers

34. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 34 Demultiplexers

35. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 35 Demultiplexers 2-line-to4-line demux2-line-to4-line demux

36. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 36 Parity Generator/Checker

37. Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 37 Parity Generators/Checkers Parity generator/checkerParity generator/checker