Digital Design Slides to accompany the textbook Digital

Digital Design Slides to accompany the textbook Digital Design, First Edition, by Frank Vahid, John Wiley and Sons Publishers, 2007. http: //www. ddvahid. com Copyright © 2007 Frank Vahid Instructors of courses requiring Vahid's Digital Design textbook (published by John Wiley and Sons) have permission to modify and use these slides for customary course-related activities, subject to keeping this copyright notice in place and unmodified. These slides may be posted as unanimated pdf versions on publicly-accessible course websites. . Power. Point source (or pdf Digital Design with animations) may not be posted to publicly-accessible websites, but may be posted for students on internal protected sites or distributed directly to students by other electronic means. Copyright © 2006 1 Instructors may make printouts of the slides available to students for a reasonable photocopying charge, without incurring royalties. Any other use requires explicit permission. Instructors Franksource Vahid may obtain Power. Point or obtain special use permissions from Wiley – see http: //www. ddvahid. com for information.

2. 2 Switches • Electronic switches are the basis of binary digital circuits – Electrical terminology • Voltage: Difference in electric potential between two points – Analogous to water pressure 4. 5 A • Current: Flow of charged particles – 9 V 4. 5 A + 2 ohms – Analogous to water flow • Resistance: Tendency of wire to resist current flow – Analogous to water pipe diameter 9 V 0 V 4. 5 A • V = I * R (Ohm’s Law) Digital Design Copyright © 2006 Frank Vahid 2

Switches • A switch has three parts control input – Source input, and output “off” • Current wants to flow from source input to output source input – Control input • Voltage that controls whether that current can flow output a control input source input “on” output (b) relay Digital Design Copyright © 2006 Frank Vahid discrete transistor vacuum tube IC quarter (to see the relative size) 3

2. 3 The CMOS Transistor • CMOS transistor – Basic switch in modern ICs a n. MOS gate 1 0 conducts does not conduct 1 0 p. MOS gate Silicon -- not quite a conductor or insulator: Semiconductor Digital Design Copyright © 2006 Frank Vahid does not conducts 4

Logic Design • Combinational Circuits – Output is function of inputs only – Design using logic gates as building block or truth table – Logic optimization • Sequential Circuits – Using combinational circuits in conjunction with memory elements (Circuits that operate one cycle at a time) – Design Using Finite State Machine and state encoding followed by combinational circuit design – Optimization such as state minimization, state encoding, etc. • Objectives – Delay, area, power, cost, etc. Digital Design Copyright © 2006 Frank Vahid 5

Boolean Logic Gates 2. 4 Building Blocks for Digital Circuits (Because Switches are Hard to Work With) • “Logic gates” are better digital circuit building blocks than switches (transistors) – Why? . . . Digital Design Copyright © 2006 Frank Vahid 6

Relating Boolean Algebra to Digital Design NOT Symbol Truth table x OR x F x 0 1 AND y F 1 0 x F x 0 0 1 1 y 0 1 F 0 1 1 1 x 0 0 1 1 0 1 y x x F F 0 0 0 1 0 y Transistor x circuit F y F F y x 0 1 y x 1 • Implement Boolean operators using transistors – Call those implementations logic gates. Digital Design Copyright © 2006 Frank Vahid 7

NOT/OR/AND Logic Gate Timing Diagrams 1 1 x x 0 y 1 F 0

Some Circuit Drawing Conventions Digital Design Copyright © 2006 Frank Vahid 9

2. 6 Representations of Boolean Functions English 1: F outputs 1 when a is 0 and b is 0, or when a is 0 and b is 1. (a) English 2: F outputs 1 when a is 0, regardless of b’s value a b F Equation 1: F(a, b) = a’b’ + a’b Equation 2: F(a, b) = a’ (c) (b) Circuit 1 a b F 0 0 1 1 1 0 0 1 1 0 Truth table a F (d) Circuit 2 The function F • A function can be represented in different ways – Above shows seven representations of the same functions F(a, b), using four different methods: English, Equation, Circuit, and Truth Table Digital Design Copyright © 2006 Frank Vahid 10

Truth Table Representation of Boolean Functions a 0 0 1 1 • Define value of F for each possible combination of input values Digital Design Copyright © 2006 Frank Vahid F (a) – 2 -input function: 4 rows – 3 -input function: 8 rows – 4 -input function: 16 rows • Q: Use truth table to define function F(a, b, c) that is 1 when abc is 5 or greater in binary b 0 1 a 0 0 1 1 b 0 0 1 1 c 0 1 0 1 (b) a a 0 0 1 1 b 0 0 1 1 c 0 1 0 1 F 0 0 0 1 1 1 F a 0 0 0 0 1 1 1 1 b 0 0 0 0 1 1 1 1 c 0 0 1 1 d 0 1 0 1 (c) 11 F

2. 7 Combinational Logic Design Process Step Description Step 1 Capture the function Create a truth table or equations, whichever is most natural for the given problem, to describe the desired behavior of the combinational logic. Step 2 Convert to equations This step is only necessary if you captured the function using a truth table instead of equations. Create an equation for each output by ORing all the minterms for that output. Simplify the equations if desired. Step 3 Implement as a gatebased circuit For each output, create a circuit corresponding to the output’s equation. (Sharing gates among multiple outputs is OK optionally. ) Digital Design Copyright © 2006 Frank Vahid 12

2. 8 More Gates NAND x NOR F y x XOR 1 XNOR y F x 0 0 1 1 • • y 0 1 F 1 1 1 0 x 0 0 1 1 y 0 1 F 1 0 0 0 x 0 0 1 1 y 0 1 F 0 1 1 0 x 0 0 1 1 y 0 1 F 1 0 0 1 F x 0 • • • y x y NAND: Opposite of AND (“NOT AND”) • NOR: Opposite of OR (“NOT OR”) XOR: Exactly 1 input is 1, for 2 -input XOR. (For more inputs -- odd number of 1 s) XNOR: Opposite of XOR (“NOT XOR”) • Digital Design Copyright © 2006 Frank Vahid NOR x y x F y 1 NAND 0 NAND same as AND with power & ground switched • Why? n. MOS conducts 0 s well, but not 1 s (reasons beyond our scope) -- so NAND more efficient Likewise, NOR same as OR with power/ground switched AND in CMOS: NAND with NOT OR in CMOS: NOR with NOT So NAND/NOR more common 13

More Gates: Example Uses • Aircraft lavatory sign example Circuit a b c S – S = (abc)’ • Detecting all 0 s – Use NOR 0 0 0 1 • Detecting equality – Use XNOR • Detecting odd # of 1 s a 0 b 0 a 1 b 1 A=B a 2 b 2 – Use XOR – Useful for generating “parity” bit common for detecting errors Digital Design Copyright © 2006 Frank Vahid 14

Completeness of NAND • Any Boolean function can be implemented using just NAND gates. Why? – – Need AND, OR, and NOT: 1 -input NAND (or 2 -input NAND with inputs tied together) AND: NAND followed by NOT OR: NAND preceded by NOTs • Likewise for NOR Digital Design Copyright © 2006 Frank Vahid 15

2. 10 Additional Considerations Schematic Capture and Simulation Inputs i 0 i 1 Outputs d 3 Simulate i 1 Outputs d 3 d 2 d 1 d 0 Simulate • Schematic capture – Computer tool for user to capture logic circuit graphically • Simulator – Computer tool to show what circuit outputs would be for given inputs • Outputs commonly displayed as waveform Digital Design Copyright © 2006 Frank Vahid 16