LN3-Logic

# LN3-Logic - FIT1001 - Computer Systems FIT1001- Computer...

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1 www.monash.edu.au FIT1001 - Computer Systems www.monash.edu.au FIT1001- Computer Systems Lecture Notes 3 Boolean Algebra and Digital Logic LN 3: FIT1001 Computer Systems 3 LN 3: Learning Objectives Truth Tables Behaviour of logic gates and combinatorial circuits Convert logic circuits into boolean expressions (& vice versa) Manipulate expressions using boolean algebra Combinatorial circuits important in computer hardware (adders, decoders, multiplexers) Using feedback to create sequential logic circuits with memory capabilities www.monash.edu.au History and technology of “Electrically Controlled Switches”

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2 LN 3: FIT1001 Computer Systems 5 History and Technology In the latter part of the nineteenth century – George Boole suggested that logical thought could be represented through mathematical equations – Computers are implementations of Boole’s Laws of Thought > John Atanasoff and Claude Shannon were among the first to see this connection Today – Relationship between electronic digital computers and human logic is well established – Digital circuits can be built from sets of simple (electrically controlled) switches – Semi-conductor material, e.g., silicon, is used for digital circuits LN 3: FIT1001 Computer Systems 6 Digital logic is based on transistors Transistors (I) Transition happens in only a few nanoseconds –How many transitions could happen in one second? Transistors are combined to form logic gates LN 3: FIT1001 Computer Systems 7 Transistors (II) “semi-conductor” Binary behaviour: off on Base V in Collector V out Emitter V cc LN 3: FIT1001 Computer Systems 8 Transistors (III) Base V in low Collector V out high Emitter V cc
3 LN 3: FIT1001 Computer Systems 9 Transistors (IV) Base V in high Collector V out low Emitter V cc LN 3: FIT1001 Computer Systems 10 Transistors (V) Base Collector Emitter Modern-day “chips” (about 3 x 3 mm in size) can contain millions of transistors V cc LN 3: FIT1001 Computer Systems 11 Gates Gate: a group of transistors Gates are switches that distinguish between two electrical voltages: – No/low voltage Æ 0 – High voltage Æ 1 Examples: AND OR NOT NAND NOR LN 3: FIT1001 Computer Systems 12 Gates: AND and OR AB 00 01 10 11 AND Gate A AND B A OR B OR Gate

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4 LN 3: FIT1001 Computer Systems 13 Gates: NOT A 0 1 NOT A NOT Gate LN 3: FIT1001 Computer Systems 14 Gates: NAND and NOR (I) AB 00 01 10 11 NAND Gate A NAND B A NOR B NOR Gate LN 3: FIT1001 Computer Systems 15 Gates and Transistors: NAND and NOR (II) Only two logical states – True/False, On/Off, 1/0 – Generally 0-1 Volts indicates “Off”, 2-5 Volts indicates “On” LN 3: FIT1001 Computer Systems 16 A AND B A B A AND B Gates and Transistors: AND A AND B A B V out
5 www.monash.edu.au Boolean Algebra LN 3: FIT1001 Computer Systems 18 Boolean Algebra Boolean algebra is a mathematical system for the manipulation of variables that can have one of two values – In formal logic, these values are True/False – In digital systems, these values are on/off, 1/0 or high/low

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## This note was uploaded on 08/15/2010 for the course FIT 1001 taught by Professor Egerton during the Three '10 term at Monash.

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LN3-Logic - FIT1001 - Computer Systems FIT1001- Computer...

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