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Lecture 4 Combinational Logic Implementation Technologies

Lecture 4 Combinational Logic Implementation Technologies. Prith Banerjee ECE C03 Advanced Digital Design Spring 1998. Outline. Review of Combinational Logic Technologies Programmable Logic Devices (PLA, PAL) MOS Transistor Logic

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Lecture 4 Combinational Logic Implementation Technologies

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  1. Lecture 4Combinational Logic Implementation Technologies Prith Banerjee ECE C03 Advanced Digital Design Spring 1998 ECE C03 Lecture 4

  2. Outline • Review of Combinational Logic Technologies • Programmable Logic Devices (PLA, PAL) • MOS Transistor Logic • READING: Katz 4.1, 4.2, Dewey 5.2, 5.3, 5.4, 5.5 5.6, 5.7, 6.2 ECE C03 Lecture 4

  3. Programmable Arrays of Logic Gates • Until now, we learned about designing Boolean functions using discrete logic gates • We will now describe a technique to arrange AND and OR gates (or NAND and NOR gates) into a general array structure • Specific functions can be programmed • Can use programmable logic arrays (PLA) or programmable array logic (PAL) ECE C03 Lecture 4

  4. PALs and PLAs Pre-fabricated building block of many AND/OR gates (or NOR, NAND) "Personalized" by making or breaking connections among the gates Programmable Array Block Diagram for Sum of Products Form ECE C03 Lecture 4

  5. Why PALs/PLAs Work Equations F0 = A + B' C' F1 = A C' + A B F2 = B' C' + A B F3 = B' C + A Key to Success: Shared Product Terms Example: Input Side: 1 = asserted in term 0 = negated in term - = does not participate Personality Matrix Output Side: 1 = term connected to output 0 = no connection to output ECE C03 Lecture 4

  6. Example of PALs and PLAs All possible connections are available before programming ECE C03 Lecture 4

  7. Example of PALs and PLAs (Contd) Unwanted connections are "blown" Note: some array structures work by making connections rather than breaking them ECE C03 Lecture 4

  8. Alternative Representations Short-hand notation so we don't have to draw all the wires! Notation for implementing F0 = A B + A' B' F1 = C D' + C' D ECE C03 Lecture 4

  9. Design Example Multiple functions of A, B, C ABC A F1 = A B C F2 = A + B + C F3 = A B C F4 = A + B + C F5 = A xor B xor C F6 = A xnor B xnor C B C A B C ABC ABC ABC ABC ABC ABC ABC ECE C03 Lecture 4 F1 F2 F3 F4 F5 F6

  10. Differences Between PALs and PLAs PAL concept — implemented by Monolithic Memories constrained topology of the OR Array A given column of the OR array has access to only a subset of the possible product terms PLA concept — generalized topologies in AND and OR planes ECE C03 Lecture 4

  11. Design Example: BCD-to-Gray Code Converter A A AB AB 00 01 11 10 00 01 11 10 CD CD 00 0 0 X 1 00 0 1 X 0 01 0 1 X 1 01 0 1 X 0 D D 0 1 X X 0 0 X X 11 11 C C 10 10 0 1 X X 0 0 X X B B K-map for W K-map for X A A AB AB 00 01 11 10 00 01 11 10 CD CD 00 0 1 X 0 00 0 0 X 1 01 0 1 X 0 01 1 0 X 0 D D 1 1 X X 0 1 X X 11 11 C C 10 10 1 1 X X 1 0 X X B B K-map for Y K-map for Z Truth Table K-maps Minimized Functions: W = A + B D + B C X = B C' Y = B + C Z = A'B'C'D + B C D + A D' + B' C D' ECE C03 Lecture 4

  12. Programmed PAL 0 0 0 0 0 0 A B C D ECE C03 Lecture 4 4 product terms per each OR gate

  13. Code Converter: Discrete Gates \ A D 1 \ D \ B \ D \ C 1: 7404 hex inverters 2,5: 7400 quad 2-input NAND \ B 3: 7410 t ri 3-input NAND 4: 7420 dual 4-input NAND \A A 1 \B 4 \C B D 2 3 W D B C 3 B 2 D C 4 4 Z A 5 B 2 1 X 2 C 1 C 3 2 Y B 1 4 SSI Packages vs. 1 PLA/PAL Package! ECE C03 Lecture 4

  14. Another Example: Magnitude Comparator A A AB AB 00 01 11 10 00 01 11 10 CD CD 00 1 0 0 0 00 0 1 1 1 01 0 1 0 0 01 1 0 1 1 D D 11 0 0 1 0 11 1 1 0 1 C C 10 0 0 0 1 10 1 1 1 0 B B K-map for EQ K-map for NE A A AB AB 00 01 11 10 00 01 11 10 CD CD 00 00 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 01 01 D D 11 1 1 0 1 11 0 0 0 0 C C 10 1 1 0 0 10 0 0 1 0 B B K-map for L T K-map for GT ABCD ABCD ABCD ABCD AC AC BD BD ABD BCD ABC BCD EQ NE LT GT ECE C03 Lecture 4

  15. Non-Gate Logic So far we have seen: AND-OR-Invert PAL/PLA Generalized Building Blocks Beyond Simple Gates Kinds of "Non-gate logic": • switching circuits built from CMOS transmission gates • multiplexer/selecter functions • decoders • tri-state and open collector gates • read-only memories ECE C03 Lecture 4

  16. Steering Logic: Switches Voltage Controlled Switches n-type Si p-type Si "n-Channel MOS" Metal Gate, Oxide, Silicon Sandwich Diffusion regions: negatively charged ions driven into Si surface Si Bulk: positively charged ions By "pulling" electrons to the surface, a conducting channel is formed ECE C03 Lecture 4

  17. Switching or Steering Logic Voltage Controlled Switches Logic 1 on gate, Source and Drain connected Logic 0 on gate, Source and Drain connected ECE C03 Lecture 4

  18. Logic Gates with Steering Logic +5V +5V +5V Logic Gates from Switches A B A B A B A A A + B NOR Gate NAND Gate Inverter Pull-up network constructed from pMOS transistors Pull-down network constructed from nMOS transistors ECE C03 Lecture 4

  19. Inverter with Steering Logic +5V +5V Inverter Operation "1" "0" "0" "1" Input is 1 Pull-up does not conduct Pull-down conducts Output connected to GND Input is 0 Pull-up conducts Pull-down does not conduct Output connected to VDD ECE C03 Lecture 4

  20. NAND Gate with Steering Logic +5V +5V NAND Gate Operation "1" "0" "1" "1" "0" "1" A = 0, B = 1 Pull-up network has path to VDD Pull-down network path broken Output node connected to VDD A = 1, B = 1 Pull-up network does not conduct Pull-down network conducts Output node connected to GND ECE C03 Lecture 4

  21. NOR Gate with Steering Logic +5V +5V NOR Gate Operation "0" "1" "0" "0" "1" "0" A = 0, B = 0 Pull-up network conducts Pull-down network broken Output node at VDD A = 1, B = 0 Pull-up network broken Pull-down network conducts Output node at GND ECE C03 Lecture 4

  22. CMOS Transmission Gate nMOS transistors good at passing 0's but bad at passing 1's pMOS transistors good at passing 1's but bad at passing 0's perfect "transmission" gate places these in parallel: Control Control Control In Out In Out In Out Control Control Control Transmission or "Butterfly" Gate Switches Transistors ECE C03 Lecture 4

  23. Selection/Demultiplexing S I 0 S Z S I 1 Selector: Choose I0 if S = 0 Choose I1 if S = 1 S S Z 0 Demultiplexer: I to Z0 if S = 0 I to Z1 if S = 1 S S I Z 1 S ECE C03 Lecture 4

  24. Use of Multiplexers or Demultiplexers A Y Demultiplexers Multiplexers B Z A Y Demultiplexers Multiplexers B Z So far, we've only seen point-to-point connections among gates Mux/Demux used to implement multiple source/multiple destination interconnect ECE C03 Lecture 4

  25. Well-formed Switching Logic Problem with the Demux implementation: multiple outputs, but only one connected to the input! S Z 0 S "0" I S S Z 1 S "0" S The fix: additional logic to drive every output to a known value Never allow outputs to "float" ECE C03 Lecture 4

  26. Complex Steering Logic Example I 1 I 1 "0" One "0" One "1" Zero "0" "1" Zero "0" N Input Tally Circuit: count # of 1's in the inputs Straight Through Diagonal Conventional Logic for 1 Input Tally Function Switch Logic Implementation of Tally Function ECE C03 Lecture 4

  27. Complex Steering Logic "0" "0" One "0" "0" One "1" Zero "0" "1" Zero "0" Operation of the 1 Input Tally Circuit Input is 0, straight through switches enabled ECE C03 Lecture 4

  28. Complex Steering Logic "1" "0" One "1" "0" One "1" Zero "0" "1" Zero "0" Operation of 1 input Tally Circuit Input = 1, diagonal switches enabled ECE C03 Lecture 4

  29. Complex Steering Logic Example I I I Zero One T wo 1 1 2 I 0 0 1 0 0 2 0 1 0 1 0 1 0 0 1 0 1 1 0 0 1 T wo Extension to the 2-input case Zero One Conventional logic implementation ECE C03 Lecture 4

  30. Complex Steering Logic Example I 1 Switch Logic Implementation: 2-input Tally Circuit I I 2 2 "0" Two Two One "0" "0" One Zero "1" Zero "0" "0" I 1 One "0" One Cascade the 1-input implementation! Zero "1" Zero "0" "0" ECE C03 Lecture 4

  31. Complex Steering Logic Operation of 2-input implementation "0" "0" "1" "0" "0" "0" "0" "0" One One "0" "1" "0" "0" Zero Zero "1" "0" "1" "1" "0" "0" "0" "0" "1" "1" "0" "1" "0" "0" "0" "1" One One "0" "1" "0" "0" Zero Zero "1" "0" "1" "0" "0" "0" "0" "0" ECE C03 Lecture 4

  32. Summary • Review of Combinational Logic Implementation Technologies • Programmable Logic Devices (PLA, PAL) • MOS Transistor Logic • NEXT LECTURE: Combinational Logic Implementation with Multiplexers, Decoders, ROMS and FPGAs • READING: Katz 4.2.2, 4.2.3, 4.2.4, 4.2.5, 10.3, Dewey 5.7 ECE C03 Lecture 4

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