Lec 11 - Implementation Technology: Look-up Tables, XOR and XNOR gates PDF

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ECE380 Digital Logic Implementation Technology: Look-up Tables, XOR and XNOR gates

Electrical & Computer Engineering

Dr. D. J. Jackson Lecture 11-1

Look-up tables • A logic block commonly used in FPGA devices is the look-up table (LUT) • An LUT contains storage cells that are used to implement small logic functions • Each cell is capable of storing a single logic value (0 or 1) • Multiplexers are used to select one of the storage cells for output • Essentially, the cells store the truth table for a function and the multiplexers select a particular cell for output based on a set of select (control) inputs

Electrical & Computer Engineering

Dr. D. J. Jackson Lecture 11-2

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Two-input LUT structure x1 0/1 0/1 f 0/1 0/1 x2 Electrical & Computer Engineering

Dr. D. J. Jackson Lecture 11-3

Programmed LUT (f=a’b+ab’) most significant variable controls last multiplexer

a 0 a 0 0 1 1

b 0 1 0 1

f 0 1 1 0

1 f 1 0 b

Electrical & Computer Engineering

Dr. D. J. Jackson Lecture 11-4

2

Three-input LUT structure x x1 2 0/1 0/1 0/1 0/1

f

0/1 0/1 0/1 0/1 x

3

Electrical & Computer Engineering

Dr. D. J. Jackson Lecture 11-5

Three-input LUT example • Show the diagram for a programmed LUT that implements the function • f(a,b,c)=a’bc+abc’+ac

Electrical & Computer Engineering

Dr. D. J. Jackson Lecture 11-6

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Exclusive OR (XOR) gate • Another basic element, very useful in building circuits that perform arithmetic operations, is the exclusive OR (XOR) gate • XOR function is denoted with the  symbol • In SOP form, a  b = ab’+a’b • Output is ‘1’ only if the inputs are different a 0 0 1 1

b 0 1 0 1

a  b 0 1 1 0

a b

Electrical & Computer Engineering

a  b

Dr. D. J. Jackson Lecture 11-7

Example XOR usage • Recall the adder circuit – sum=xy’+x’y – carry=xy

Electrical & Computer Engineering

Dr. D. J. Jackson Lecture 11-8

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XOR of three variables • What is the canonical SOP form for the following expression? f(a,b,c) = a  b  c

Electrical & Computer Engineering

Dr. D. J. Jackson Lecture 11-9

Exclusive NOR (XNOR) gate • Derived from the XOR function, XNOR is the complement of XOR • XNOR function is denoted with the  symbol • In SOP form, a  b = (a  b)’ = ab+a’b’ • Output is ‘1’ only if the inputs are the same • Also called an equivalence function a 0

b 0

a  b 1

0

1

0

1

0

0

1

1

1

Electrical & Computer Engineering

a b

a  b

Dr. D. J. Jackson Lecture 11-10

5

XNOR of three variables • What is the canonical SOP form for the following expression? f(a,b,c) = a  b  c

Electrical & Computer Engineering

Dr. D. J. Jackson Lecture 11-11

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