ECE 616 Advanced FPGA Designs - Electrical and Computer Engineering University of Western Ontario

ECE 616 Advanced FPGA Designs Electrical and Computer Engineering University of Western Ontario General Welcome remark Digital and analog VLSI: ASIC and FPGA Overview 06/06/18 Course Requirement Rules Attendance Projects: Final 06/06/18 Information Text book in library:  M J S Smith, Application-Specific Integrated Circuits, Addison-Wesley, 1997 ISBN: 0201500221  Digital Systems Design Using VHDL, Charles H Roth, Jr., PWS Publishing, 1998 (ISBN: 0-534-95099-X) Class notes and lab manual: www.engga.uwo.ca/people/wwang 06/06/18 Wei Wang Office: EC 1006 Office hours: Thursday 3:00 to 5:00 pm Email: 06/06/18 wwang@eng.uwo.ca Digital and Analog 06/06/18 06/06/18 06/06/18 Overview • Digital system: 489 materials • VHDL • FPGA and CPLD 06/06/18 Outline Review of Logic Design Fundamentals • Combinational Logic • Boolean Algebra and Algebraic Simplifications • Karnaugh Maps 06/06/18 10 Basic Logic Gates 06/06/18 12 Full Adder Module Truth table Algebraic expressions F(inputs for which the Minterms function is 1): Sum  X' Y' Cin  X' YCin'XY' Cin'XYCin Cout  X' YCin  XY' Cin  XYCin'XYCin m-notation Sum m1  m2  m4  m7  m(1, 2, 4, 7) Cout m3  m5  m6  m7  m(3, 5, 6, 7) 06/06/18 13 Full Adder (cont’d) Module Truth table Algebraic expressions F(inputs for which the Maxterms function is 0): Sum ( X  Y  Cin)( X  Y'Cin' )( X' Y  Cin' )( X' Y'Cin) Cout ( X  Y  Cin)( X  Y  Cin' )( X  Y'Cin)( X'Y  Cin) M-notation Sum M1 M3 M5 M6 M(1, 3, 5, 6) Cout M0 M1 M2 M4 M(0, 1, 2, 4) 06/06/18 14 Boolean Algebra • Basic mathematics used for logic design • Laws and theorems can be used to simplify logic functions – Why we want to simplify logic functions? 06/06/18 15 Laws and Theorems of Boolean Algebra 06/06/18 16 Laws and Theorems of Boolean Algebra 06/06/18 17 Simplifying Logic Expressions • Combining terms – Use XY+XY’=X, X+X=X Cout  X' YCin  XY' Cin  XYCin'XYCin ( X' YCin  XYCin)  ( XY' Cin  XYCin)  ( XYCin' XYCin)  YCin  XCin  XY • Eliminating terms – Use X+XY=X • Eliminating literals – Use X+X’Y=X+Y • Adding redundant terms – Add 0: XX’ – Multiply with 1: (X+X’) 06/06/18 18 Theorems to Apply to Exclusive-OR X  X X   X' X  X 0 X  X' 1 X  Y Y  X (Commutative law) ( X  Y)  Z  X  ( Y  Z) (Associative law) X( Y  Z)  XY  XZ (Distributive law) ( X  Y)'  X  Y'  X'Y  XY  X' Y' 06/06/18 19 Karnaugh Maps • Convenient way to simplify logic functions of 3, 4, 5, (6) variables • Four-variable K-map Location of minterms – each square corresponds to one of the 16 possible minterms – - minterm is present; (or blank) – minterm is absent; – X – don’t care • the input can never occur, or • the input occurs but the output is not specified – adjacent cells differ in only one value => can be combined 06/06/18 20 Karnaugh Maps (cont’d) • Example 06/06/18 21 Sum-of-products Representation • Function consists of a sum of prime implicants • Prime implicant – a group of one, two, four, eight 1s on a map represents a prime implicant if it cannot be combined with another group of 1s to eliminate a variable • Prime implicant is essential if it contains a that is not contained in any other prime implicant 06/06/18 22 Selection of Prime Implicants Two minimum forms 06/06/18 23 Procedure for Sum of products • Choose a minterm (a 1) that has not been covered yet • Find all 1s and Xs adjacent to that minterm • If a single term covers the minterm and all adjacent 1s and Xs, then that term is an essential prime implicant, so select that term • Repeat steps 1, 2, until all essential prime implicants have been chosen • Find a minimum set of prime implicants that cover the remaining 1s on the map If there is more than one such set, choose a set with a minimum number of literals 06/06/18 24 Products of Sums • F(1) = {0, 2, 3, 5, 6, 7, 8, 10, 11} F(X) = {14, 15} 06/06/18 25 To Do • Textbook – Chapter 1.1, 1.2 • Read – Altera’s MAX+plus II and the UP1 Educational board: A User’s Guide, B E Wells, S M Loo – Altera University Program Design Laboratory Package 06/06/18 26 ... way to simplify logic functions of 3, 4, 5, (6) variables • Four-variable K-map Location of minterms – each square corresponds to one of the 16 possible minterms – - minterm is present; (or blank)... Karnaugh Maps (cont’d) • Example 06/06/18 21 Sum -of- products Representation • Function consists of a sum of prime implicants • Prime implicant – a group of one, two, four, eight 1s on a map represents... Integrated Circuits, Addison-Wesley, 1997 ISBN: 0201500221  Digital Systems Design Using VHDL, Charles H Roth, Jr., PWS Publishing, 1998 (ISBN: 0-5 3 4-9 5099-X) Class notes and lab manual: www.engga.uwo.ca/people/wwang