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R. Anderson

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T, 1 True F,0 False

p, q, r propositions

conjunction

˜ negation

conditionalit

↔ bi-conditionally

==> implication

equivalence

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function is a listing of all possibleassignments of values to the variables of the

unction; an next to eac assignment is t e

value the function takes under that

A convenient way to represent the operation

of a digital circuit as columns of input values

and their corresponding output responses.

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P Q P Q  P Q 

T T T T

T F T F

F T T F

F F F F

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Analo

Derived from the word analogy which means“quantity related to”, or “resembles”, or“corresponds” to another quantity

Example:

The length of a column of mercury in a thermometer is

an analog of the temperature because the length of themercury s propor ona o e empera ure.

An analog variable can have any value between itsmaximum and minimum limits.

    -to +10, X may assume any one of an infinite numberof values within this range.

 value by an arbitrarily small amount

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and in time.All variables in a digital system must take a

value chosen from a set of values called an

alphabet  van age o g a epresen a on

Data resistant to error

Thou h the si nal can be distorted if the distortion

doesn’t convert the symbol into another symbol in the

alphabet then is relatively easy to recognize and

reconstitute the original symbol.

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symbols called 1 and 0 Also referred to as:

true and false

on and off 

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or logic levels. The advantages of digital techniques stem

from the fact it is easier to get an electronic

device to switch into one of two states, than

of values.

Di ital electronics or an di ital circuit are

usually made from large assemblies of logic

gates, simple electronic representations of

oo ean og c unc ons.

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elements called Gates. The word gate conveys the idea of a two-

state device – open or shut.

A gate may be thought of as a black box withone or more npu erm na s an an ou pu

terminal.

 

system or object when it is viewed primarily in

terms of its input and output characteristics.

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input terminals and produce a digital signalat its output terminal

The type of gate determines the actual

processing involved.  e ou pu o a ga e w wo npu

terminals A and B can be expressed

al ebraicall as:

C = F(A,B)

Where A, B, C are two valued variables and F is a

logical function.

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AND OR

NOT

er ve

NAND

EOR

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output The output of an AND gate is true if and only if

each of its input is also in a true state

Conversely if one or more of the inputs to the

AND ate is false then the out ut will be false.

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 =

B = 0000111100001011

A B = 00001011

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Either A or B Both A and B

The output of the OR gate is true if:  ny one or more o ts nput s true

 A

B

out

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 =

B = 0010010110111101

A B = 10111101

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Inverter Complementer

This is a two-terminal device with a single

input and a single output  I t e input to t e inverter is X t en t e

output is NOT X written :

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the opposite of the input

 A

The output is

the logical

of the inputInput A = 10101010

nver er u pu :

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gate followed by an INVERTER The NOR (NotOR ) gate is derived from a OR

gate followed by and inverter

NAND Gate

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NAND #2 10101010

NOR #1 01010101NOR #2 00000000

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In di ital circuits a fli -flo is a term

referring to an electronic circuit (a bistablemultivibrator) that has two stable states and

memory.

RS FLIP FLOP