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Unit 9 Multiplexers, Decoders, and Programmable Logic DevicesPowerPoint Presentation

Unit 9 Multiplexers, Decoders, and Programmable Logic Devices

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### Unit 9Multiplexers, Decoders, and Programmable Logic Devices

Ku-Yaw Chang

Assistant Professor, Department of Computer Science and Information Engineering

Da-Yeh University

Contents

9.1 Introduction

9.2 Multiplexers

9.3 Three-State Buffers

9.4 Decoders and Encoders

9.5 Read-Only Memories

9.6 Programmable Logic Devices

9.7 Complex Programmable Logic Devices

9.8 Field Programmable Gate Arrays

Fundamentals of Logic Design

Programmable Logic Devices

- A general name for a digital integrated circuit capable of being programmed to provide a variety of different logic functions

Fundamentals of Logic Design

Programmable Logic Arrays

- Performs the same basic function as a ROM
- n inputs and m outputs
- m functions of n variables

- n inputs and m outputs
- Differences in internal organization
- The decoder is replaced with an AND array
- OR array
- PLA : a sum-of-product expression
- ROM : truth table

Fundamentals of Logic Design

PLA Structure

Fundamentals of Logic Design

PLA with Three Inputs, Five Product Terms, and Four Outputs

Fundamentals of Logic Design

AND-OR Array

Fundamentals of Logic Design

PLA Table

Fundamentals of Logic Design

PLA Realization

- f1 = a’bd + abd + ab’c’ + b’c
- f2 = c + a’bd
- f3 = bc + ab’c’ + abd

Fundamentals of Logic Design

PLA Structure

Fundamentals of Logic Design

PLA Table v.s. Truth Table

- PLA Table
- Each row represents a general product term.
- 0, 1, or more rows may be selected.

- ROM Truth Table
- Each row represents a minterm.
- Exactly one row will be selected.

Fundamentals of Logic Design

PLAs

- Mask-programmable PLAs
- Programmed at the time of manufacture
- Similar to mask-programmable ROM

- Field-programmable PLAs (FPLAs)
- Use electronic charges to store a pattern in the AND and OR arrays
- An FPLA with 16 inputs, 48 product terms and 8 outputs
- 8 functions of 16 variables
- Total number of product terms does not exceed 48

Fundamentals of Logic Design

Programmable Array Logic

- PAL
- a special case of PLA
- AND array is programmable
- OR array is fixed

- Less expensive
- Easier to program

- a special case of PLA

Fundamentals of Logic Design

PAL segment

Fundamentals of Logic Design

Full Adder

- The logic equations for the full adder are
Sum = X’Y’Cin + X’YC’in + XY’C’in + XYCin

Cout = XCin + YCin + XY

Fundamentals of Logic Design

Full Adder

Fundamentals of Logic Design

Contents

9.1 Introduction

9.2 Multiplexers

9.3 Three-State Buffers

9.4 Decoders and Encoders

9.5 Read-Only Memories

9.6 Programmable Logic Devices

9.7 Complex Programmable Logic Devices

9.8 Field Programmable Gate Arrays

Fundamentals of Logic Design

CPLDs

- As integrated circuit technology continues to improve, more and more gates can be placed on a single chip.
- Complex Programmable Logic Devices (CPLDs)

- When storage elements such as flip-flops are also included on the same IC, a small digital system can be implemented with a single CPLD.

Fundamentals of Logic Design

Contents

9.1 Introduction

9.2 Multiplexers

9.3 Three-State Buffers

9.4 Decoders and Encoders

9.5 Read-Only Memories

9.6 Programmable Logic Devices

9.7 Complex Programmable Logic Devices

9.8 Field Programmable Gate Arrays

Fundamentals of Logic Design

Field Programmable Gate Arrays

- FPGA
- An IC contains an array of identical logic cells with programmable interconnections

- The user can program
- Functions realized by each logic cell
- Connections between the cells

Fundamentals of Logic Design

FPGA

Fundamentals of Logic Design

Configurable Logic Block

- CLB
- Two function generators
- Four inputs
- Can implement any function of up to four variables
- Implemented as lookup tables (LUTs)

- Two flip-flops
- Various multiplexers for routing signals within the CLB

- Two function generators

Fundamentals of Logic Design

Simplified CLB

Fundamentals of Logic Design

Implementation of a LUT

Fundamentals of Logic Design

Decomposition of Switching Functions

- To implement a switching function of more than four variables using 4-variable function generator
- The function must be decomposed into subfunctions
- Each subfunction requires only four variables

Fundamentals of Logic Design

Shannon’s Expansion Theorem

- Expand a function of the variables a,b,c, and d about the variable a :
f(a,b,c,d) = a’ f(0,b,c,d) + af(1,b,c,d)

= a’ f0 + af1

- f0 = f(0,b,c,d): replace a with 0 in f(a,b,c,d)
- f1 = f(1,b,c,d): replace a with 1 in f(a,b,c,d)

Fundamentals of Logic Design

Expansion Example

f(a,b,c,d)

= c’d’ + a’b’c + bcd + ac’

= a’ (c’d’ + b’c + bcd) + a (c’d’ + bcd + c’)

= a’ (c’d’ + b’c + cd) + a (c’ + bd)

= a’ f0 + af1

Fundamentals of Logic Design

Expansion Example

Fundamentals of Logic Design

Shannon’s Expansion Theorem

- General form : expanding an n-variable function about the variables xi :
f(x1 , x2 ,…, xi-1 , xi ,xi+1 ,…, xn)

= xi ’ f(x1 , x2 ,…, xi-1 , 0,xi+1 ,…, xn) + xi f(x1 , x2 ,…, xi-1 , 1,xi+1 ,…, xn)

= xi ’ f0 + xi f1

Fundamentals of Logic Design

5-variable function

f(a, b, c, d, e)

= a’ f(0, b, c, d, e) + af(1, b, c, d, e)

= a’ f0 + af1

- Any 5-variable function can be realized using two 4-variable function generators and a 2-to-1 MUX.

Fundamentals of Logic Design

5- and 6-variable functions

Fundamentals of Logic Design

Supplement

- SIP
- Single In-line Package

- DIP
- Dual In-line Package

- PGA
- Pin Grid Array

- SIMM
- Single In-line Memory Module

- DIMM
- Dual In-line Memory Module

Fundamentals of Logic Design

IEEE Standard 1164 defines a std_logic type that has nine values:

U : Uninitialized

X : Unknown

0 : Logic 0 (driven)

1 : Logic 1 (driven)

Z : High impedance

W : Weak 1

L : Logic 0 (read)

H : Logic 1 (read)

- : Don’t care

SupplementFundamentals of Logic Design

Homework #3 values:

- 9.7
- 9.8
- 9.13

- 9.1
- 9.2
- 9.3
- 9.4

Paper Submission, due on April 8, 2004.

Late submission will not be accepted.

Fundamentals of Logic Design

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