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Chapter 3 Digital Logic Structures. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 3-2 Transistor: Building.

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Presentation on theme: "Chapter 3 Digital Logic Structures. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 3-2 Transistor: Building."— Presentation transcript:

1 Chapter 3 Digital Logic Structures

2 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 3-2 Transistor: Building Block of Computers Microprocessors contain millions of transistors Intel Pentium II: 7 million Compaq Alpha 21264: 15 million Intel Pentium III: 28 million Intel Pentium4: 55 Million Intel Core 2 Duo: 291 Million Logically, each transistor acts as a switch Combined to implement logic functions AND, OR, NOT Combined to build higher-level structures Adder, multiplexor, decoder, register, … Combined to build processor LC-3

3 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Transistors 3-3 First transistor: Bell Labs in 1947; developed by J. Bardeen, W. Shockley & W. Brattain A 2011 processor with 1.17 billion transistors positioned in 240 sq. millimeters

4 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 3-4 Simple Switch Circuit Switch open: No current through circuit Light is off V out is +2.9V Switch closed: Short circuit across switch Current flows Light is on V out is 0V Switch-based circuits can easily represent two states: on/off, open/closed, voltage/no voltage.

5 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 3-5 N-type MOS Transistor MOS = Metal Oxide Semiconductor two types: N-type and P-type N-type when Gate has positive voltage, short circuit between #1 and #2 (switch closed) when Gate has zero voltage, open circuit between #1 and #2 (switch open) Gate = 1 Gate = 0 Terminal #2 must be connected to GND (0V). Animation Drain Source GND

6 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 3-6 P-type MOS Transistor P-type is complementary to N-type when Gate has positive voltage, open circuit between #1 and #2 (switch open) when Gate has zero voltage, short circuit between #1 and #2 (switch closed) Gate = 1 Gate = 0 Terminal #1 must be connected to +2.9V. Source Drain GND +2.9V

7 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 3-7 CMOS Circuit Complementary MOS Uses both N-type and P-type MOS transistors P-type Attached to + voltage Pulls output voltage UP when input is zero N-type Attached to GND Pulls output voltage DOWN when input is one For all inputs, make sure that output is either connected to GND or to +, but not both!

8 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 3-8 Inverter (NOT Gate) InOut 0 V2.9 V 0 V InOut Truth table High Voltage Ground

9 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Logical Operations In 1850, George Boole developed Boolean Algebra showing that all logical functions can be performed with just 3 operations (AND, OR & NOT). In 1937, Claude Shannon showed that Boolean Algebra could be applied to circuit design. 3-9

10 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display NOR Gate (NOT OR) ABC Note: Serial structure on top, parallel on bottom. High Voltage Ground

11 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display OR Gate Add inverter to NOR. ABC

12 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display NAND Gate (NOT-AND) ABC Note: Parallel structure on top, serial on bottom.

13 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display AND Gate Add inverter to NAND. ABC

14 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Basic Logic Gates

15 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display More than 2 Inputs? AND/OR can take any number of inputs. AND = 1 if all inputs are 1. OR = 1 if any input is 1. Similar for NAND/NOR. An AND gate with k inputs is called and ANDk gate (e.g., an AND2, AND3, etc). Can implement AND3 with multiple AND2 gates, or with single transistor circuit. AND/OR are associative and commutative -- combine in any order.

16 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Logical Completeness Can implement ANY truth table with AND, OR, NOT. ABCD AND combinations that yield a "1" in the truth table. Put a bubble (inverter) for every 0, a straight- in for every 1 in a row 2. OR the results of the AND gates. If there are N 1s, there will be N and gates; the or gate will have N inputs

17 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display DeMorgan's Law Converting AND to OR (with some help from NOT) Consider the following gate: AB Same as A OR B! To convert AND to OR (or vice versa), invert inputs and output.

18 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Summary MOS transistors are used as switches to implement logic functions. N-type: connect to GND, turn on (with 1) to pull down to 0 P-type: connect to +2.9V, turn on (with 0) to pull up to 1 Basic gates: NOT, NOR, NAND Logic functions are usually expressed with AND, OR, and NOT Properties of logic gates Completeness can implement any truth table with AND, OR, NOT DeMorgan's Law convert AND to OR by inverting inputs and output


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