1 / 32

ETE 204 - Digital Electronics

ETE 204 - Digital Electronics. Multiplexers, Decoders and Encoders. [Lecture:10] Instructor: Sajib Roy Lecturer, ETE, ULAB. Multiplexers. ● A multiplexer has. - 2 n data inputs. - n control inputs. - 1 output.

quant
Download Presentation

ETE 204 - Digital Electronics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ETE 204 - Digital Electronics Multiplexers, Decoders and Encoders [Lecture:10] Instructor: Sajib Roy Lecturer, ETE, ULAB

  2. Multiplexers ● A multiplexer has - 2n data inputs - n control inputs - 1 output ● A multiplexer routes (or connects) the selecteddata input to the output. - The value of the control inputs determines the data input that is selected. Summer2012 ETE 204 - Digital Electronics 2

  3. Multiplexers Data inputs Z = A′.I0 + A.I1 Control input Summer2012 ETE 204 - Digital Electronics 3

  4. Multiplexers A B Z 0 0 I0 0 1 I1 1 0 I2 20 1 1 I 3 21 m0 = A'.B' m1 = A'.B MSB LSB m2 = A.B' m3 = A.B Z = A′.B'.I0 + A'.B.I1 + A.B'.I2 + A.B.I3 Summer2012 ETE 204 - Digital Electronics 4

  5. Multiplexers A B C Z m0 0 0 0 I0 m1 0 0 1 I1 m2 0 1 0 I2 m3 0 1 1 I3 m4 1 0 0 I4 m5 1 0 1 I5 1 11 1 m6m7 0 I 6 20 1 I 7 22 MSB LSB Z = A′.B'.C'.I0 + A'.B'.C.I1 + A'.B.C'.I2 + A'.B.C.I3 + A.B'.C'.I0 + A.B'.C.I1 + A'.B.C'.I2 + A.B.C.I3 Summer2012 ETE 204 - Digital Electronics 5

  6. Multiplexers 20 2n-1 Z =  mi.Ii Summer2012 ETE 204 - Digital Electronics 6

  7. Decoders ● A decoder has - n inputs - 2n outputs ● A decoder selects one of 2n outputs by decoding the binary value on the n inputs. ● The decoder generates all of the minterms ofthe n input variables. - Exactly one output will be active for each combination of the inputs. What does “active” mean? Summer2012 ETE 204 - Digital Electronics 7

  8. Decoders Z0 A Z1Z2Z3 2-to-4 Zi = mi Decoder msb B active-high output A B Z0 Z1 Z2 Z3 m0 0 0 1 0 0 0 m1 0 1 0 1 0 0 m2 1 0 0 0 1 0 1 1 0 0 0 1 m3 Summer2012 ETE 204 - Digital Electronics 8

  9. Decoders Z0 A Z1Z2Z3 2-to-4 Zi = (mi)' = Mi Decoder msb B active-low output A B Z0 Z1 Z2 Z3 M0 0 0 0 1 1 1 M1 0 1 1 0 1 1 M2 1 0 1 1 0 1 1 1 1 1 1 0 M3 Summer2012 ETE 204 - Digital Electronics 9

  10. Decoders msb 3-to-8 Decoder Summer2012 ETE 204 - Digital Electronics 10

  11. Decoder with Enable AB Z0Z1Z2Z3 2-to-4 Decoder with Enable En active-high enable En A B Z0 Z1 Z2 Z3 1 0 0 1 0 0 0 1 0 1 0 1 0 0 enabled 1 1 0 0 0 1 0 1 1 1 0 0 0 1 disabled 0 x x 0 0 0 0 Summer2012 ETE 204 - Digital Electronics 11

  12. Decoder with Enable AB Z0Z1Z2Z3 2-to-4 Decoder with Enable En active-low enable En A B Z0 Z1 Z2 Z3 0 0 0 1 0 0 0 0 0 1 0 1 0 0 enabled 0 1 0 0 0 1 0 0 1 1 0 0 0 1 disabled 1 x x 0 0 0 0 Summer2012 ETE 204 - Digital Electronics 12

  13. Encoders ● An encoder has - 2n inputs - n outputs ● Outputs the binary value of the selected(or active) input. ● Performs the inverse operation of a decoder. ● Issues - What if more than one input is active? - What if no inputs are active? Summer2012 ETE 204 - Digital Electronics 13

  14. Encoders Y0Y1Y2Y3 A 4-to-2 Encoder B Y0 Y1 Y2 Y3 A B 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 1 1 Summer2012 ETE 204 - Digital Electronics 14

  15. Priority Encoders ● If more than one input is active, the higher-orderinput has priority over the lower-order input. - The higher value is encoded on the output ● A valid indicator, d, is included to indicate whether ornot the output is valid. - Output is invalid when no inputs are active ● d = 0 - Output is valid when at least one input is active ● d = 1 Why is the valid indicator needed? Summer2012 ETE 204 - Digital Electronics 15

  16. Priority Encoders msb 8-to-3PriorityEncoder Valid bit Summer2012 ETE 204 - Digital Electronics 16

  17. Using a 2n-input Multiplexer ● Use a 2n-input multiplexer to realize a logic circuit fora function with 2n minterms. - n = # of control inputs = # of variables in the function● Each minterm of the function can be mapped to adata input of the multiplexer. ● For each row in the truth table, for the function,where the output is 1, set the corresponding datainput of the multiplexer to 1. - That is, for each minterm in the minterm expansion of thefunction, set the corresponding input of the multiplexer to 1. ● Set the remaining inputs of the multiplexer to 0. Summer2012 ETE 204 - Digital Electronics 17

  18. Using an 2n-input Mux Example: Using an 8-to-1 multiplexer, design a logic circuit to realize the following Boolean function F(A,B,C) = m(2, 3, 5, 6, 7) Summer2012 ETE 204 - Digital Electronics 18

  19. Using an 2n-input Mux Example: Using an 8-to-1 multiplexer, design a logic circuit to realize the following Boolean function F(A,B,C) = m(1, 2, 4) Summer2012 ETE 204 - Digital Electronics 19

  20. Using an 2(n-1)-input Multiplexer ● Use a 2(n-1)-input multiplexer to realize a logic circuitfor a function with 2n minterms. - n - 1 = # of control inputs; n = # of variables in function ● Group the rows of the truth table, for the function, into 2(n-1) pairs of rows. - Each pair of rows represents a product term of (n - 1)variables. - Each pair of rows is mapped to one data input of the mux.● Determine the logical function of each pair of rows interms of the remaining variable. - If the remaining variable, for example, is x, then the possible values are x, x', 0, and 1. 20 Summer2012 ETE 204 - Digital Electronics

  21. Using an 2(n-1)-input Mux Example: F(x,y,z) = m(1, 2, 6, 7) Summer2012 ETE 204 - Digital Electronics 22

  22. Using an 2(n-1)-input Mux Example: F(A,B,C,D) = m(1,3,4,11,12-15) Summer2012 ETE 204 - Digital Electronics 22

  23. Using a 2(n-2)-input Mux A similar design approach can be implemented using a 2(n-2)-input multiplexer. Summer2012 ETE 204 - Digital Electronics 23

  24. Circuit Design using Decoders Summer2012 ETE 204 - Digital Electronics 24

  25. Using an n-output Decoder ● Use an n-output decoder to realize a logic circuit for afunction with n minterms. ● Each minterm of the function can be mapped to anoutput of the decoder. ● For each row in the truth table, for the function, wherethe output is 1, sum (or “OR”) the correspondingoutputs of the decoder. - That is, for each minterm in the minterm expansion of thefunction, OR the corresponding outputs of the decoder. ● Leave remaining outputs of the decoder unconnected. Summer2012 ETE 204 - Digital Electronics 25

  26. Using an n-output Decoder Example: Using a 3-to-8 decoder, design a logic circuit to realize the following Boolean function F(A,B,C) = m(2, 3, 5, 6, 7) Summer2012 ETE 204 - Digital Electronics 26

  27. Using an n-output Decoder Example: Using two 2-to-4 decoders, design a logic circuit to realize the following Boolean function F(A,B,C) = m(0, 1, 4, 6, 7) Summer2012 ETE 204 - Digital Electronics 27

  28. Hierarchical Design ● Several issues arise when designing large multiplexers and decoders (as 2-level circuits). - Number of logic gates gets prohibitively large - Number of inputs to each logic gate (i.e. fan-in) gets prohibitively large ● Instead, design both hierarchically - Use smaller elements as building blocks - Interconnect building blocks in a multi-tier structure Summer2012 ETE 204 - Digital Electronics 28

  29. Hierarchical Design Exercise: Design an 8-to-1 multiplexer using4-to-1 and 2-to-1 multiplexers only. Summer2012 ETE 204 - Digital Electronics 29

  30. Hierarchical Design Exercise: Design a 16-to-1 multiplexer using 4-to-1 multiplexers only. Summer2012 ETE 204 - Digital Electronics 30

  31. Hierarchical Design Exercise: Design a 4-to-16 decoder using 2-to-4 decoders only. Summer2012 ETE 204 - Digital Electronics 31

  32. Questions? Summer2012 ETE 204 - Digital Electronics 32

More Related