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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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