1. Trang chủ
  2. » Công Nghệ Thông Tin

Digital logic design

251 824 0

Đang tải... (xem toàn văn)

Tài liệu hạn chế xem trước, để xem đầy đủ mời bạn chọn Tải xuống

THÔNG TIN TÀI LIỆU

Thông tin cơ bản

Định dạng
Số trang 251
Dung lượng 3,94 MB

Nội dung

1 Dr. D. J. Jackson Lecture 1-1Electrical & Computer Engineering ECE380 Digital Logic Introduction Dr. D. J. Jackson Lecture 1-2Electrical & Computer Engineering Digital hardware • Logic circuits are used to build computer hardware as well as other products (digital hardware) • Late 1960’s and early 1970’s saw a revolution in digital capability – Smaller transistors – Larger chip size • More transistors/chip gives greater functionality, but requires more complexity in the design process 2 Dr. D. J. Jackson Lecture 1-3Electrical & Computer Engineering Digital hardware • Integrated circuits are fabricated on silicon wafers • Wafers are cut & packaged to form individual chips • Chips have from tens to millions of transistors Dr. D. J. Jackson Lecture 1-4Electrical & Computer Engineering How complex is a digital design? • Complexity can, and generally does, surpass human capability – 16 million transistors/cm 2 now – 100 million transistors/cm 2 in 10 years (?) • Provides motivation for computer-based design techniques • Most engineering work is done with CAD packages 3 Dr. D. J. Jackson Lecture 1-5Electrical & Computer Engineering Two design approaches •Traditional – Relies on mathematical models – Analytical approaches – Provides insight and understanding of problem – Useful for small problems – Inadequate for large (real) problems •CAD – Software relies on mathematical model and analytical approach – Transparent to user – Many details are abstracted – Useful/required for real problems Dr. D. J. Jackson Lecture 1-6Electrical & Computer Engineering Traditional versus CAD design • CAD tool usage is essential • Insight and basic understanding offered by traditional approach is still important – Initial conceptualization is still traditional – Effective use of CAD tools requires some understanding of what the tools are doing – Use of design options requires insight 4 Dr. D. J. Jackson Lecture 1-7Electrical & Computer Engineering Types of chips •Standard chips – Contain a small amount of circuitry (<100 transistors) – Performs simple functions – 7400 series devices • Programmable logic devices (PLD) – Collection of gates with programmable interconnections – Function is configurable by designer/user – Design with PLD is via a CAD tool Dr. D. J. Jackson Lecture 1-8Electrical & Computer Engineering Types of chips •Custom-designed chips – Optimized for a specific task – better performance – Larger amount of logic circuitry – Cost of production is high – Large volume required to justify cost 5 Dr. D. J. Jackson Lecture 1-9Electrical & Computer Engineering A field-programmable gate array Memory block Group of 8 logic cells Interconnection wires Dr. D. J. Jackson Lecture 1-10Electrical & Computer Engineering The development process (1) Design Correct? Required Product Define specifications Initial design Simulation Redesign no 6 Dr. D. J. Jackson Lecture 1-11Electrical & Computer Engineering The development process (2) Prototype implementation Testing Make corrections Meets specs? Minor errors? Redesign Finished product no no yes yes Dr. D. J. Jackson Lecture 1-12Electrical & Computer Engineering What should you expect to gain from this course? • Understanding of concepts, models, algorithms and processes for digital logic design – Relevance of the material to subsequent courses and to your career • Problem solving skills – Formulating and attacking new problems – Need to struggle with problems – evolve your problem solving skills • Communicate solutions in a clear, concise manner 1 Dr. D. J. Jackson Lecture 2-1Electrical & Computer Engineering ECE380 Digital Logic Introduction to Logic Circuits: Variables, functions, truth tables, gates and networks Dr. D. J. Jackson Lecture 2-2Electrical & Computer Engineering Logic circuits • Logic circuits perform operations on digital signals – Implemented as electronic circuits where signal values are restricted to a few discrete values •Inbinary logic circuits there are only two values, 0 and 1 • The general form of a logic circuit is a switching network Switching Network X 1 X 2 X 3 X m Y 1 Y 2 Y 3 Y n discrete values 2 Dr. D. J. Jackson Lecture 2-3Electrical & Computer Engineering Boolean algebra • Direct application to switching networks – Work with 2-state devices Æ 2-valued Boolean algebra (switching algebra) – Use a Boolean variable (X, Y, etc.) to represent an input or output of a switching network – Variable may take on only two values (0, 1) –X=0, X=1 – These symbols are not binary numbers, they simply represent the 2 states of a Boolean variable – They are not voltage levels, although they commonly refer to the low or high voltage input/output of some circuit element Dr. D. J. Jackson Lecture 2-4Electrical & Computer Engineering Variables and functions • The simplest binary element is a switch that has two states • If the switch is controlled by x, we say the switch is open if x =0 and closed if x =1 x 1 = x 0 = (a) Two states of a switch S x (b) Symbol for a switch 3 Dr. D. J. Jackson Lecture 2-5Electrical & Computer Engineering Variables and functions • Assume the switch controls a lightbulb as shown – The output is defined as the state of the light L • If the light is on -> L=1 • If the light is off -> L=0 • The state of L, as function of x is – L(x)=x •L(x) is a logic function • x is an input variable (a) Simple connection to a battery S x (b) Using a ground connection as the return path L Battery Light x Power supply S L Dr. D. J. Jackson Lecture 2-6Electrical & Computer Engineering Variables and functions (AND) • Consider the possibility of two switches controlling the state of the light • Using a series connection, the light will be on only if both switches are closed –L(x 1 , x 2 )= x 1 · x 2 – L=1 iff (if and only if) x 1 AND x 2 are 1 The logical AND function (series connection) S x 1 L Power supply S x 2 Light “·” AND operator The circuit implements a logical AND function x 1 · x 2 =x 1 x 2 4 Dr. D. J. Jackson Lecture 2-7Electrical & Computer Engineering Variables and functions (OR) • Using a parallel connection, the light will be on only if either or both switches are closed –L(x 1 , x 2 )= x 1 + x 2 –L=1 if x 1 OR x 2 is 1 (or both) S x 1 L Power supply S x 2 The logical OR function (parallel connection) Light “+” OR operator The circuit implements a logical OR function Dr. D. J. Jackson Lecture 2-8Electrical & Computer Engineering Variables and functions • Various series-parallel connections would realize various logic functions –L(x 1 , x 2 , x 3 )= (x 1 + x 2 )· x 3 S x 1 L Power supply S x 2 Light S x 3 [...]... Computer Engineering f’= ΠM Dr D J Jackson Lecture 4-16 8 ECE380 Digital Logic Introduction to Logic Circuits: Design Examples Electrical & Computer Engineering Dr D J Jackson Lecture 5-1 Design examples • Logic circuits provide a solution to a problem • Some may be complex and difficult to design • Regardless of the complexity, the same basic design issues must be addressed 1 Specify the desired behavior... f(a,b,c)=(a’+b)c – f(a,b,c)=a’b+c Electrical & Computer Engineering Dr D J Jackson Lecture 3-17 9 ECE380 Digital Logic Introduction to Logic Circuits: Synthesis using AND, OR, and NOT gates Electrical & Computer Engineering Dr D J Jackson Lecture 4-1 Example logic circuit design • Assume we want to design a logic circuit with three inputs x, y, and z • The circuit output should be 1 only when x=1 and either... 1 Dr D J Jackson Lecture 2-14 7 Logic gates and networks • Each basic logic operation (AND, OR, NOT) can be implemented resulting in a circuit element called a logic gate • A logic gate has one or more inputs and one output that is a function of its inputs x1 x2 x1 x2 x1 ⋅ x2 ⋅ … ⋅ xn x1 ⋅ x2 xn AND gates Electrical & Computer Engineering Dr D J Jackson Lecture 2-15 Logic gates and networks x1 x2 x1... Electrical & Computer Engineering Dr D J Jackson Lecture 2-16 8 Logic gates and networks • A larger circuit is implemented by a network of gates – Called a logic network or logic circuit x x x 1 2 f = (x + x ) ⋅ x 1 2 3 3 Electrical & Computer Engineering Dr D J Jackson Lecture 2-17 Logic gates and networks • Draw the truth table and the logic circuit for the following function – F(a,b,c) = ac+bc’ a... function could be written as – f(x,y,z)=xy’z+xyz’+xyz • sum of products form Electrical & Computer Engineering Dr D J Jackson Lecture 4-2 1 Example logic circuit design Electrical & Computer Engineering Dr D J Jackson Lecture 4-3 Example logic circuit design • Implements f correctly, f(x,y,z)=xy’z+xyz’+xyz but is not the simplest such network xy’z+xyz’+xyz xy’z+xy from 14a y z f x 0 0 0 0 x(y’z+y)... Jackson Lecture 2-18 9 Analysis of a logic network • To determine the functional behavior of a logic network, we can apply all possible input signals to it x x 0→ 0→1→ 1 1→ 1→0→ 0 1 A 0→ 1→0→ 1 0→ 0→0→ 1 1→1→ 0→ 1 f B 2 Network that implements = x1 + x1 ⋅ x2 f Electrical & Computer Engineering Dr D J Jackson Lecture 2-19 Analysis of a logic network • The function of a logic network can also be described... manipulation can be used to simplify Boolean expressions – Simpler expression => simpler logic circuit • Not practical to deal with complex expressions in this way • However, the theorems & properties provide the basis for automating the synthesis of logic circuits in CAD tools – To understand the CAD tools the designer should be aware of the fundamental concepts Electrical & Computer Engineering Dr... by a timing diagram (gives dynamic behavior of the network) 1 x 1 0 x 1 2 0 A 1 0 B 1 0 f 1 0 Time Timing diagram Electrical & Computer Engineering Dr D J Jackson Lecture 2-20 10 ECE380 Digital Logic Introduction to Logic Circuits: Boolean algebra Electrical & Computer Engineering Dr D J Jackson Lecture 3-1 Axioms of Boolean algebra • Boolean algebra: based on a set of rules derived from a small number... xy’z+xy from 14a y z f x 0 0 0 0 x(y’z+y) from 12a 0 1 0 0 x(y+z) from 16a 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 Electrical & Computer Engineering Dr D J Jackson Lecture 4-4 2 Example logic circuit design • Obviously, the cost (in terms of gates and connections) of this network is much less than the initial network • The process of generating a circuit from a stated desired functional behavior... OR and AND operations are often called the logical sum and product operations • The expression – ABC+A’BD+ACE’ – Is a sum of three product terms • The expression – (A+B+C)(A’+B+D)(A+C+E’) – Is a product of three sum terms Electrical & Computer Engineering Dr D J Jackson Lecture 3-15 Precedence of operations • In the absence of parentheses, operations in a logical expression are performed in the order . Engineering ECE380 Digital Logic Introduction to Logic Circuits: Variables, functions, truth tables, gates and networks Dr. D. J. Jackson Lecture 2-2Electrical & Computer Engineering Logic circuits • Logic. 1-1Electrical & Computer Engineering ECE380 Digital Logic Introduction Dr. D. J. Jackson Lecture 1-2Electrical & Computer Engineering Digital hardware • Logic circuits are used to build computer. & Computer Engineering Logic gates and networks • Each basic logic operation (AND, OR, NOT) can be implemented resulting in a circuit element called a logic gate • A logic gate has one or more

Ngày đăng: 27/03/2014, 20:00

TỪ KHÓA LIÊN QUAN