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

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

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

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

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.

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

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

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

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??

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

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

SYEN 3330 Digital Systems Chapter4-1 Page 12 Multiplexers

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

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

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

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

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

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

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 Z Y 8-to-1 MUX 8-to-1 MUX D3D3 D2D2 D1D1 D0D0 S1S1 S0S0 S2S2 D4D4 D5D5 D6D6 D7D7

SYEN 3330 Digital Systems Chapter4-1 Page 20 Other MUX Implementations A C B Y D0D0 D1D1 D2D2 D3D A C B Z D0D0 D1D1 D2D2 D3D AA AA AA

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

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

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

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

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