Multiplexers Decoders ROMs (LUTs) Page 1

Size: px

Start display at page:

Download "Multiplexers Decoders ROMs (LUTs) Page 1"

Egbert Bradley
6 years ago
Views:

1 Multiplexers Decoders ROMs (LUTs) Page

2 A Problem Statement Design a circuit which will select between two inputs (A and B) and pass the selected one to the output (Q). The desired circuit is called a multiplexer or MUX for short Page 2

3 Multiplexers s a b q ab s q = s a + sb a s b q Page 3

4 Multiplexer Symbols Preferred symbol a q a q b b s s Page 4

5 Data Steering a b q a b q a b q s Key idea: the select input wire selects one of the inputs and passes it out to the output. Page 5

6 Multiplexers Data Inputs { I I I 2 I 3 4-to- MUX Z A B Control Inputs Z = A B I + A BI + AB I 2 + ABI 3 Page 6

7 8 to Multiplexer I I Data Inputs I 2 I 3 I 4 8-to- MUX Z I 5 I 6 I 7 A B C Control Inputs Z = A B C I + A B CI + A BC I 2 + Page 7

8 A General MUX n Data Inputs I I I n- n: MUX Z Output s k-. s log 2 (n) Control Inputs Page 8

9 MUXes In A Microprocessor They are each 6-bits wide A 6-bit wide MUX is simply 6 -bit wide MUXes all with common s inputs Page 9

10 6-bit 3: MUX Example BusA bit bit BusB Select control lines bit BusC bit Page

11 6-bit 3: MUX Example BusA BusB BusC bit bit bit 5 Output s s They all use the same select control lines One bit from each bus goes to each MUX The result is a 6-bit bus Page

12 Implementing Logic with MUX Blocks Page 2

13 Example A B C F A= part of the truth table when A=, F= A= part of the truth table whena=, F=B+C B+C A F Page 3

14 Example 2 B A C F B= part of the truth table whenb=, F=AC B= part of the truth table whenb=, F=A AC A B F Page 4

15 Example 3 C A B F C= part of the truth table whenc=, F=AB C= part of the truth table whenc=, F=A AB A C F All 3 of these examples are the same truth table Page 5

16 Using a Bigger MUX A B C F AB= part of the truth table whenab=, F= AB= part of the truth table whenab=, F=C AB= part of the truth table whenab=, F= AB= part of the truth table whenab=, F=C C C AB F Can easily re-order truth table to use different MUX control inputs Page 6

17 Another 4: MUX Example AB F F AB This shows that a large enough MUX can directly implement a truth table Page 7

18 Implementing Logic Functions With Muxes Implement: Z = A B + BC A B I C I I 2 4-to- MUX Z I 3 for AB=, Z= A B Page 8

19 Implementing Logic Functions With Muxes Implement: Z = A B + BC A B I C I I 2 4-to- MUX Z I 3 for AB=, Z= A B Page 9

20 Implementing Logic Functions With Muxes Implement: Z = A B + BC A B I C I I 2 4-to- MUX Z C I 3 for AB=, Z=C A B Page 2

21 Implementing Logic Functions With Muxes Implement: Z = A B + BC A B I C I I 2 4-to- MUX Z C I 3 A B Page 2

22 Implementing Logic Functions With Muxes An alternate method Z = A B + BC A= B= Z = + C = I A= B= Z = + C = I 4-to- MUX Z A= B= Z = + C = I 2 A= B= Z = + C = C C I 3 A B Page 22

23 Implementing Logic Functions With Muxes Z (A,B,C,D) = Σ m(3,5,,,2,5) + Σ d (4,8,4) A B C D 3 2 X X X 8 Page 23

24 Implementing Logic Functions With Muxes Z (A,B,C,D) = Σ m(3,5,,,2,5) + Σ d (4,8,4) A B C D D I I X X I 2 I 3 8-to- MUX Z I 4 I 5 I 6 X I 7 A B C Page 24

25 Implementing Logic Functions With Muxes Z (A,B,C,D) = Σ m(3,5,,,2,5) + Σ d (4,8,4) A B C D X X D I I I 2 I 3 8-to- MUX Z I 4 I 5 I 6 X I 7 A B C Page 25

26 Implementing Logic Functions With Muxes Z (A,B,C,D) = Σ m(3,5,,,2,5) + Σ d (4,8,4) A B C D X X D I I I 2 I 3 I 4 I 5 8-to- MUX Z I 6 X I 7 A B C Page 26

27 Implementing Logic Functions With Muxes Z (A,B,C,D) = Σ m(3,5,,,2,5) + Σ d (4,8,4) A B C D X X X D D I I I 2 I 3 I 4 I 5 I 6 I 7 8-to- MUX Z A B C Page 27

28 Implementing Logic Functions With Muxes Z (A,B,C,D) = Σ m(3,5,,,2,5) + Σ d (4,8,4) A B C D B I I X X I 2 I 3 8-to- MUX Z I 4 I 5 I 6 X I 7 A C D Page 28

29 Implementing Logic Functions With Muxes Z (A,B,C,D) = Σ m(3,5,,,2,5) + Σ d (4,8,4) A B C D X X B B I I I 2 I 3 8-to- MUX Z I 4 I 5 I 6 X I 7 A C D Page 29

30 Implementing Logic Functions With Muxes Z (A,B,C,D) = Σ m(3,5,,,2,5) + Σ d (4,8,4) A B C D X X B B I I I 2 I 3 I 4 I 5 8-to- MUX Z I 6 X I 7 A C D Page 3

31 Implementing Logic Functions With Muxes Z (A,B,C,D) = Σ m(3,5,,,2,5) + Σ d (4,8,4) A B C D X X X B B I I I 2 I 3 I 4 I 5 I 6 I 7 8-to- MUX Z A C D Page 3

32 Implementing Logic Functions With Muxes An alternate method A B C D X X X Z = AC + AD + A BC + B CD B B I I I 2 I 3 I 4 I 5 I 6 I 7 8-to- MUX Z A C D Page 32

33 Implementing Logic Functions With Muxes An alternate method A C D Z = AC + AD + A BC + B CD Z = ()() + ()() + ()B() + B ()() = B Z = ()() + ()() + ()B() + B ()() = B Z = ()() + ()() + ()B() + B ()() = Z = ()() + ()() + ()B() + B ()() = B Z = ()() + ()() + ()B() + B ()() = Z = ()() + ()() + ()B() + B ()() = Z = ()() + ()() + ()B() + B ()() = Z = ()() + ()() + ()B() + B ()() = Page 33

34 Implementing Logic Functions With Muxes An alternate method A C D New Method Original Method Z = B Z = Z = B Z = B Z = Z = Z = B Z = B Z = Z = Why are they different? Z = Z = Z = Z = Z = Z = Page 34

35 Implementing Logic Functions With Muxes An alternate method A B C D X X The original method used this grouping. It was determined to be. X Z = AC + AD + A BC + B CD Page 35

36 Implementing Logic Functions With Muxes An alternate method A B C D X X The new method used this grouping. It was determined to be. X Z = AC + AD + A BC + B CD Page 36

37 Implementing Logic Functions With Muxes An alternate method A B C D X X The new method used this grouping. It was determined to be. Which is right?? X Z = AC + AD + A BC + B CD Page 37

38 Implementing Logic Functions With Muxes An alternate method A B C D X X The new method used this grouping. It was determined to be. X Which is right?? They both are!!!! Z = AC + AD + A BC + B CD Page 38

39 Implementing Logic Functions With Muxes An alternate method A B C D / X X For A= C= D= If A BC D = then input = If A BC D = then input = B They are both right!!! Page 39

40 Implementing Logic Functions With Muxes Z (A,B,C,D) = Σ m(3,5,,,2,5) + Σ d (4,8,4) A B C D B I X X I 4-to- MUX Z I 2 I 3 X A C Page 4

41 Implementing Logic Functions With Muxes Z (A,B,C,D) = Σ m(3,5,,,2,5) + Σ d (4,8,4) A B C D B I X X D I I 2 4-to- MUX Z I 3 X A C Page 4

42 Implementing Logic Functions With Muxes Z (A,B,C,D) = Σ m(3,5,,,2,5) + Σ d (4,8,4) A B B I C D X X B' D D I I 2 4-to- MUX Z I 3 X F = B D A C Page 42

43 Implementing Logic Functions With Muxes An alternate method A C Z = AC + AD + A BC + B CD Z = ()() + ()D + ()B() + B ()D = B Z = ()() + ()D + ()B() + B ()D = B D Z = ()() + ()D + ()B() + B ()D = D Z = ()() + ()D + ()B() + B ()D = Same as before! Page 43

44 Decoders Page 44

45 2:4 Decoder A B Q Q Q2 Q3 A B 2:4 Decode Q Q Q2 Q3 Q = A B Q = A B Q2 = AB Q3 = AB m m m2 m3 A decoder is a minterm generator Page 45

46 3:8 Decoder A B C QQQ2Q3Q4Q5Q6Q7 Q = A B C Q = A B C Q7 = ABC 3:8 Decoder m m m7 Page 46

47 Implementing Logic With Decoders 2:4 Decode F = Σ m(, 2) 2:4 Decode F = Π M(, 2) 2:4 Decode F = Σ m(, 3) Historically, some decoders have come with inverted outputs Page 47

48 Uses of Decoders Decode 3-bit op-code into a set of 8 signals op op op2 3:8 Decoder Add Sub And Xor Not Load Store Jump Page 48

49 ROM: Read-Only Memory Can read values from it Cannot write to it Address Data Address In 8 x ROM Data Out Address Data x 5 ROM Page 49

50 Read Only Memory (ROM) Each minterm of each function can be specified 3 Inputs Lines A B C ROM 8 words x 5 bits F F F 2 F 3 F 4 5 Outputs Lines A B C F F F 2 F 3 F 4 When you program a ROM, you are specifying these Page 5

51 ROM View # An addressable memory Send in address (addr n ) Receive data stored at that location (w n ) Can have multi-bit data addr2 addr addr 8 x 5 ROM w4 w3 w2 w w Page 5

52 ROM View #2 A hardware implementation of a truth table A B C F A B B C 8 x ROM F Page 52

53 ROM Two Different Views Both views are accurate Page 53

54 ROM Internal Structure n Input Lines. n:2 n decoder... Memory Array 2 n words x m bits... m Output Lines Page 54

55 ROM Memory Array V V V V V Resistors pull outputs down to GND if no row wires drive them high A B C 3:8 Decoder m =A B C m =A B C m 2 =A BC m 3 =A BC m 4 =AB C m 5 =AB C m 6 =ABC m 7 =ABC F F F 2 F 3 F 4 F = m + m4 + m7 F = m + m + m2 + m5 A diode a one-way resistor Page 55

56 ROM Technologies: Not Always Diode-Based Program Only Once Mask programmable Fusible Link Re-Programmable EPROM (ultraviolet erase) EE-PROM (electrically erase) Flash memory Beyond the scope of this class Page 56

57 Using a ROM For Logic F = AB + A BC G = A B C + C H = AB C + ABC + A B C A B C F G H Page 57

58 Using a ROM For Logic F = AB + A BC G = A B C + C H = AB C + ABC + A B C A B C F G H Page 58

59 Using a ROM For Logic F = AB + A BC G = A B C + C H = AB C + ABC + A B C A B C F G H Just fill out the truth table CAD tools usually do the rest Page 59

60 Using ROM for Combinational Logic A B C D Q ROM6X A a3 B a2 C a INIT=???? D a ROM6X is a Xilinx cell Insert it into schematics like any other primitive Set its contents by double-clicking on inserted cell in schematic. Page 6

61 Using ROM for Combinational Logic A B C D Q 8 4 D A B C D ROM6X a3 a2 a a INIT=84D Page 6

62 ROM Types in Xilinx ROM6X = 4-input LUT Specify INIT contents with 4-digit HEX value ROM32X = 5-input LUT Specify INIT contents with 8-digit HEX value Page 62

Unit 9. Multiplexers, Decoders, and Programmable Logic Devices. Unit 9 1

Unit 9. Multiplexers, Decoders, and Programmable Logic Devices. Unit 9 1 Unit 9 Multiplexers, ecoders, and Programmable Logic evices Unit 9 Outline Multiplexers Three state buffers ecoders Encoders Read Only Memories (ROMs) Programmable logic devices ield Programmable Gate