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Chapter 3 Digital Logic Structures Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 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 3-2 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Transistors http://www.brew-wood.co.uk/computers/transistor.htm 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 3-3 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Simple Switch Circuit Switch open: • No current through circuit • Light is off • Vout is +2.9V Switch closed: • • • • Short circuit across switch Current flows Light is on Vout is 0V Switch-based circuits can easily represent two states: on/off, open/closed, voltage/no voltage. 3-4 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 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 Drain Animation Source Gate = 0 GND Terminal #2 must be connected to GND (0V). GND 3-5 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 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) +2.9V Gate = 1 GND Source Gate = 0 Terminal #1 must be connected to +2.9V. Drain 3-6 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 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! 3-7 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Inverter (NOT Gate) High Voltage Truth table Ground In Out 0 V 2.9 V 2.9 V 0V In Out 0 1 1 0 3-8 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Logical Operations http://www.computerhistory.org/revolution/digital-logic/12/269 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 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. NOR Gate (NOT OR) High Voltage Ground Note: Serial structure on top, parallel on bottom. A B C 0 0 1 0 1 0 1 0 0 1 1 0 3-10 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. OR Gate A B C 0 0 0 0 1 1 1 0 1 1 1 1 Add inverter to NOR. 3-11 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. NAND Gate (NOT-AND) Note: Parallel structure on top, serial on bottom. A B C 0 0 1 0 1 1 1 0 1 1 1 0 3-12 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. AND Gate A B C 0 0 0 0 1 0 1 0 0 1 1 1 Add inverter to NAND. 3-13 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Basic Logic Gates 3-14 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. A B A B C C A B C 3-15 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Logical Completeness Can implement ANY truth table with AND, OR, NOT. A B C D 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 A B C 1.AND combinations that yield a "1" in the truth table. Put a “bubble” (inverter) for every 0, a straightin for every 1 in a row 2. OR the results of the AND gates. D If there are N 1’s, there will be N and gates; the or gate will have N inputs 3-16 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: A B A B A B A B 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 0 1 1 1 0 0 0 1 To convert AND to OR (or vice versa), invert inputs and output. Same as A OR B! 3-17 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 3-18