digital logic and computer design ppt

digital logic design lectures ppt and digital logic design ppt slides
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Dr.DouglasPatton,United States,Teacher
Published Date:26-07-2017
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ECE 545—Digital System Design with VHDL Lecture 1 Digital Logic Review 1 Lecture Roadmap – Combinational Logic •  Basic Logic Review •  Basic Gates •  DeMorgan’s Law •  Combinational Logic Blocks •  Multiplexers •  Decoders, Demultiplexers •  Encoders, Priority Encoders •  Half Adders, Full Adders •  Multi-Bit Combinational Logic Blocks •  Multi-bit multiplexers •  Multi-bit adders •  Comparators 2 Lecture Roadmap – Sequential Logic •  Sequential Logic Building Blocks •  Latches, Flip-Flops •  Sequential Logic Circuits •  Registers, Shift Registers, Counters •  Memory (RAM, ROM) 3 Textbook References •  Combinational Logic Review •  Stephen Brown and Zvonko Vranesic, Fundamentals of Digital nd rd Logic with VHDL Design, 2 or 3 Edition •  Chapter 2 Introduction to Logic Circuits (2.1-2.8 only) •  Chapter 6 Combinational-Circuit Building Blocks (6.1-6.5 only) •  OR your undergraduate digital logic textbook (chapters on combinational logic) •  Sequential Logic Review •  Stephen Brown and Zvonko Vranesic, Fundamentals of Digital nd rd Logic with VHDL Design, 2 or 3 Edition •  Chapter 7 Flip-flops, Registers, Counters, and a Simple Processors (7.3-7.4, 7.8-7.11 only) •  OR your undergraduate digital logic textbook (chapters on sequential logic) 4 Basic Logic Review some slides modified from: S. Dandamudi, “Fundamentals of Computer Organization and Design” 5 Basic Concepts •  Simple logic gates •  AND  0 if one or more inputs is 0 •  OR  1 if one or more inputs is 1 •  NOT •  NAND = AND + NOT •  1 if one or more inputs is 0 •  NOR = OR + NOT •  0 if one or more input is 1 •  XOR implements exclusive-OR function •  NAND and NOR gates require fewer transistors than AND and OR in standard CMOS •  Functionality can be expressed by a truth table •  A truth table lists output for each possible input combination 6 Basic Logic Gates 7 Number of Functions •  Number of functions •  With N logical variables, we can define N 2 2 functions •  Some of them are useful •  AND, NAND, NOR, XOR, … •  Some are not useful: •  Output is always 1 •  Output is always 0 •  “Number of functions” definition is useful in proving completeness property 8 Complete Set of Gates •  Complete sets •  A set of gates is complete •  if we can implement any logical function using only the type of gates in the set •  Some example complete sets •  AND, OR, NOT Not a minimal complete set •  AND, NOT •  OR, NOT •  NAND •  NOR •  Minimal complete set •  A complete set with no redundant elements. 9 NAND as a Complete Set •  Proving NAND gate is universal 10 Logic Functions •  Logical functions can be expressed in several ways: •  Truth table •  Logical expressions •  Graphical form •  HDL code •  Example: •  Majority function •  Output is one whenever majority of inputs is 1 •  We use 3-input majority function 11 Logic Functions (cont’d) Truth table Logical expression form F = A B + B C + A C A B C F Graphical schematic form 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 12 Boolean Algebra Boolean identities Name AND version OR version . Identity x 1 = x x + 0 = x . Complement x x’ = 0 x + x’ = 1 . . Commutative x y = y x x + y = y + x . . Distribution x (y+z) = xy+xz x + (y z) = (x+y) (x+z) . Idempotent x x = x x + x = x . Null x 0 = 0 x + 1 = 1 13 Boolean Algebra (cont’d) •  Boolean identities (cont’d) Name AND version OR version Involution x = (x’)’ - . . Absorption x (x+y) = x x + (x y) = x . . . . Associative x (y z) = (x y) z x + (y + z) = (x + y) + z . . de Morgan (x y)’ = x’ + y’ (x + y)’ = x’ y’ (de Morgan’s law in particular is very useful) 14 Majority Function Using Other Gates •  Using NAND gates •  Get an equivalent expression A B + C D = (A B + C D)’’ •  Using de Morgan’s law . A B + C D = ( (A B)’ (C D)’)’ •  Can be generalized •  Example: Majority function . . A B + B C + AC = ((A B)’ (B C)’ (AC)’)’ 15 Majority Function Using Other Gates (cont'd) •  Majority function 16 Combinational Logic Building Blocks Some slides modified from: S. Dandamudi, “Fundamentals of Computer Organization and Design” S. Brown and Z. Vranesic, "Fundamentals of Digital Logic" 17 Multiplexers log n selection inputs 2 n inputs 1 output •  multiplexer •  n binary inputs (binary input = 1-bit input) •  log n binary selection inputs 2 •  1 binary output •  Function: one of n inputs is placed onto output •  Called n-to-1 multiplexer 18 2-to-1 Multiplexer s f s w 0 0 w 0 0 f w 1 1 w 1 1 (b) Truth table (a) Graphical symbol w w 0 0 s f s w 1 w 1 f (d) Circuit with transmission gates (c) Sum-of-products circuit Source: Brown and Vranesic 19 4-to-1 Multiplexer s 0 s s s f 1 1 0 w 00 0 w 0 0 0 w 01 1 w 0 1 1 f w 10 2 w 1 0 2 w 11 3 w 1 1 3 (a) Graphic symbol (b) Truth table s 0 w 0 s 1 w 1 f w 2 w 3 Source: Brown and Vranesic (c) Circuit 20

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