1. SYEN 3330 Digital SystemsJung H. Kim Chapter 4-1 1 SYEN 3330 Digital Systems Chapter 4 -Part 1

2. SYEN 3330 Digital Systems Chapter4-1 Page 2 Functional Block: Decoders

3. SYEN 3330 Digital Systems Chapter4-1 Page 3 2-to-4 Line Decoder

4. SYEN 3330 Digital Systems Chapter4-1 Page 4 2-to-4 Line Demultiplexer

5. SYEN 3330 Digital Systems Chapter4-1 Page 5 Example: 74F138 Demultiplexer Note: This "Truth Table" uses the "x" to mean "this could be either 0 or 1". Thus, it "compacts" some of 2 6 = 64 lines.

6. SYEN 3330 Digital Systems Chapter4-1 Page 6 Implementing Logic with Decoders

7. SYEN 3330 Digital Systems Chapter4-1 Page 7 Example 1: F(A,B) =  m(0,3) B A F m0m0 m3m3

8. SYEN 3330 Digital Systems Chapter4-1 Page 8 Example 1: F(X,Y,Z) =  m(0,3,5,6)

9. SYEN 3330 Digital Systems Chapter4-1 Page 9 Implementing Larger Minterms S0S0 S1S1 D3D3 D2D2 D1D1 D0D0 S0S0 S1S1 D3D3 D2D2 D1D1 D0D0 A B C D m 15 m0m0 m??

10. SYEN 3330 Digital Systems Chapter4-1 Page 10 Functional Block: Encoders

11. SYEN 3330 Digital Systems Chapter4-1 Page 11 Review: Decoders and Encoders

12. SYEN 3330 Digital Systems Chapter4-1 Page 12 Multiplexers

13. SYEN 3330 Digital Systems Chapter4-1 Page 13 Example: A 4-to-1 multiplexer S0S0 S1S1 I3I3 I2I2 I1I1 I0I0 X

14. SYEN 3330 Digital Systems Chapter4-1 Page 14 Multiplexer Versus Decoder Note how similar the two are internally. S0S0 S1S1 I3I3 I2I2 I1I1 I0I0 X

15. SYEN 3330 Digital Systems Chapter4-1 Page 15 Functions with Multiplexers

16. SYEN 3330 Digital Systems Chapter4-1 Page 16 Example: Gray to Binary Code

17. SYEN 3330 Digital Systems Chapter4-1 Page 17 Gray to Binary (Continued)

18. SYEN 3330 Digital Systems Chapter4-1 Page 18 Gray to Binary (Continued)

19. SYEN 3330 Digital Systems Chapter4-1 Page 19 Gray to Binary (Continued) A B D3D3 D2D2 D1D1 D0D0 S1S1 S0S0 S2S2 D4D4 D5D5 D6D6 D7D7 Out C A B C 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 Z Y 8-to-1 MUX 8-to-1 MUX D3D3 D2D2 D1D1 D0D0 S1S1 S0S0 S2S2 D4D4 D5D5 D6D6 D7D7

20. SYEN 3330 Digital Systems Chapter4-1 Page 20 Other MUX Implementations A C B Y 1 1 1 1 00011011 D0D0 D1D1 D2D2 D3D3 0 0 0 0 A C B Z 0 1 0 1 00011011 D0D0 D1D1 D2D2 D3D3 0 11 0 AA AA AA

21. SYEN 3330 Digital Systems Chapter4-1 Page 21 MUX Implementations (Cont.) D3D3 D2D2 D1D1 D0D0 S1S1 S0S0 B Out C D3D3 D2D2 D1D1 D0D0 S1S1 S0S0 B C A' 1 1 A A 0 0 Z Y 4-to-1 MUX 4-to-1 MUX

22. SYEN 3330 Digital Systems Chapter4-1 Page 22 MUX: (Cont.) Factoring Out C

23. SYEN 3330 Digital Systems Chapter4-1 Page 23 MUX: (Cont.) Factoring out B

24. SYEN 3330 Digital Systems Chapter4-1 Page 24 MUX: (Cont.) Factoring out A

25. SYEN 3330 Digital Systems Chapter4-1 Page 25 Summary Know the functions performed by the following functional blocks: Decoders Demultiplexers Encoders Multiplexers Know how to implement Boolean functions using: Multiplexers Decoders