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EE207: Digital Systems I, Semester I 2003/2004

EE207: Digital Systems I, Semester I 2003/2004. CHAPTER 6-i: Programmable Logic Devices (PLDs). Overview. Three-State Buffers Programmable Logic Technologies Read-Only Memory (ROM) Programmable Logic Arrays (PLAs) Programmable Array Logic (PAL). Three-State Buffers.

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EE207: Digital Systems I, Semester I 2003/2004

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  1. EE207: Digital Systems I, Semester I 2003/2004 CHAPTER 6-i: Programmable Logic Devices (PLDs)

  2. Overview • Three-State Buffers • Programmable Logic Technologies • Read-Only Memory (ROM) • Programmable Logic Arrays (PLAs) • Programmable Array Logic (PAL) Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  3. Three-State Buffers • Buffer output has 3 states: 0, 1, Z • Z stands for High-Impedance  Open circuit EN = 0  out = Z (open circuit) EN = 1  out = in (regular buffer) EN out in Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  4. Three-state buffer(BUF)/inverter(INV) symbols EN EN out out in in 3-state BUF, EN high 3-state INV, EN high EN EN out out in in 3-state BUF, EN low 3-state INV, EN low Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  5. Multiplexed output lines using three-state buffers • Assume an output line that can receive data from either a system (circuit) A or a system B. A If A = B  out = A = B If A  B  a large enough current can be created, that causes excessive heating and could damage the circuit. out B wiredlogic Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  6. ENA A out ENB B S A 0 out B 1 S Multiplexed output lines using three-state buffers (cont.) • Solution: A B Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  7. Programmable Logic Devices (PLDs) • Standard logic devices that can be programmed to implement any combinational logic circuit. • Standard  of regular structure • Programmed  refers to a hardware process used to specify the logic that a PLD implements Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  8. Gate Symbols . . . . . . Conventional AND gate symbol Array Logic OR gate symbol One major difference! a b c F = 0 a F b c F = a.c F = a.b.c Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  9. Read-Only Memory (ROM) • Stores binary information permanently • Non-Volatile (info is kept even when power is turned off) k inputs = specify the # of addresses available n outputs = specify the size of data ROM 2k x n m k Block Diagram Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  10. Read-Only Memory (cont.) Address 8x4 ROM • Example: k=3, n=4 • There are 23=8 available addresses • 4-bits are stored in each address 3 4 Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  11. ROM construction: Example of an 25x8 ROM • Use a 5-to-32 decoder to generate the 32 addresses. • Use 8 OR gates, each can be programmed to be driven by any of the decoder outputs. Programmable logic. # of interconnectionsis 25x8 Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  12. Programming the ROM, i.e. load desired data at specified addresses Address (in decimal) 0 1 2 3 28 29 30 31 ROM addresses ROM data Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  13. Programming the ROM (cont.) Example: Let I0I1I3I4 = 00010 (address 2). Then, output 2 of the decoder will be 1, the remaining outputs will be 0, and ROM output becomes A7A6A5A4A3A2A1A0 = 11000101. Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  14. ROM-based circuit implementation • Given a 2kxn ROM, we can implement ANY combinational circuit with at most k inputs and at most n outputs. • Why? • k-to-2k decoder will generate all 2k possible minterms • Each of the OR gates must implement a m() • Each m() can be programmed Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  15. Example • Find a ROM-based circuit implementation for: • f(a,b,c) = a’b’ + abc • g(a,b,c) = a’b’c’ + ab + bc • h(a,b,c) = a’b’ + c • Solution: • Express f(), g(), and h() in m()format (use truth tables) • Program the ROM based on the 3 m()’s Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  16. Example (cont.) • There are 3 inputs and 3 outputs, thus we need a 8x3 ROM block. • f = m(0, 1, 7) • g = m(0, 3, 6, 7) • h = m(0, 1, 3, 5, 7) a 0 1 2 3 4 5 6 7 3-to-8decoder b c g f h Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  17. Programmable Logic Arrays (PLAs) • Similar concept as in ROM, except that a PLA does not necessarily generate all possible minterms (ie. the decoder is not used). • More precisely, in PLAs both the AND and OR arrays can be programmed (in ROM, the AND array is fixed – the decoder – and only the OR array can be programmed). Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  18. OR array AND array PLA Example • f(a,b,c) = a’b’ + abc • g(a,b,c) = a’b’c’ + ab + bc • h(a,b,c) = c • PLAs can be more compact • implementations than ROMs, • since they can benefit from • minimizing the number • of products required to • implement a function Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  19. Another PLA Example • Find a PLA-based circuit implementation for: • F1(A,B,C) = AB’ + AC + A’BC’ • F2(A,B,C) = (AC + BC)’ • Solution: • 3 inputs, 2 outputs ( 2 OR gates) • 4 distinct product terms (4 AND gates) • Use XOR array to find complements Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  20. PLA Example (cont.) XOR array F1 F2’ Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  21. PLA Example (cont.) Tabular Form Specification of interconnection programming F1 = AB’+AC+A’BC’ F2 = AC+BC Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  22. Determining the size of a PLA • Given: • n inputs • p product terms • m outputs • PLA size is: • Gates: n INV (and maybe n BUF) + p ANDs + m ORs + m XORs • Programmable interconnections: 2np + pm + 2m Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  23. Programmable Array Logic (PAL) • OR plane (array) is fixed, AND plane can be programmed • Less flexible than PLA • # of product terms available per function (OR outputs) is limited Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  24. inputs 1st output section Only functions with at most four products can be implemented 2nd output section 3rd output section 4th output section PAL Example Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  25. PAL-based circuit implementation W = ABC + CD X = ABC + ACD + ACD + BCD Y = ACD + ACD + ABD Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  26. Can we implement more complex functions using PALs? • Yes, by allowing output lines to also serve as input lines in the AND plane. Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  27. Example • Implement the combinational circuit described by the following equations, using a PAL with 4 inputs, 4 outputs, and 3-wide AND-OR structure. • W(A,B,C,D) = m(2,12,13) • X(A,B,C,D) = m(7,8,9,10,11,12,13,14,15) • Y(A,B,C,D) = m(0,2,3,4,5,6,7,8,10,11,15) • Z(A,B,C,D) = m(1,2,8,12,13) Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  28. Example (cont.) • Use function simplification techniques to derive: • W = ABC’+A’B’CD’ • X = A+BCD • Y=A’B+CD+B’D’ • Z=ABC’+A’B’CD’+AC’D’+A’B’C’D = W + AC’D’+A’B’C’D Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  29. Example (cont.) Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

  30. Example (cont.) Tabular Form Specification of interconnection programming Chapter 6-i: Programmable Logic Devices (6.5 -- 6-8)

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