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Digital Systems

Introduction

Binary Quantities and Variables

Logic Gates

Boolean Algebra Combinational Logic

Number Systems and Binary Arithmetic

Numeric and Alphabetic Codes

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Introduction

Digital systems are concerned with digital signals

Digital signals can take many forms

Here we will concentrate on binary signals sincethese are the most common form of digital signals

can be used individually

perhaps to represent a single binary quantity or the state of a

single switch can be used in combination

to represent more complex quantities

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Binary Quantities and Variables

A binary quantity is one that can take only 2 states

9.2

A simple binary arrangement

S LOPEN OFF

CLOSED ON

S L0 01 1A truth table

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A binary arrangement with two switches in series

L = S1 AND S2

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A binary arrangement with two switches in parallel

L = S1 OR S2

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Three switches in series

L = S1 AND S2AND S3

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Three switches in parallel

L = S1 OR S2OR S3

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A series/parallel arrangement

L = S1 AND (S2OR S3)

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Representing an unknown network

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Logic Gates

A logic gate is an electronic circuit/device which makes

the logical decisions.

The building blocks used to create digital circuits are

logic gates

There are three elementary logic gates and a range of

other simple gates

Each gate has its own logic symbol which allows

complex functions to be represented by a logic diagram

The function of each gate can be represented by a truth

table or using Boolean notation

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The AND gate

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The OR gate

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The NOT gate (or inverter)

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A logic buffer gate

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The NAND gate

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The NOR gate

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The Exclusive OR gate

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The Exclusive NOR gate

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Realization of other gates from NAND andNOR

The universality of the NAND gate means that it canbe used :

as an inverter and that combinations of NAND gates

can be used to implement the AND, OR, and NORoperations.

Similarly, the NOR gate can be used to implementthe inverter (NOT), AND, OR, and NAND operations.

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NAND Gate as a Universal Gate Element

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NOR Gate as a Universal Gate Element

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