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Mark P. Melegrito, PECE

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Objectives

 

Differentiate and simplify the formsof 

Boolean epression, applying the

basic theorems and properties ofBoolean !lgebra and implement them

in logic circ"its.

Differentiate the types of Boolean

epressions.

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Canonical and #tandard $orms

Minterms%#tandard

Prod"ct&

Materms

%#tandard #"m&

' ( Primed ' ( )nprimed

* ( )nprimed * ( Primed

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Minterms Maxtermsx y z Term Designation Term Designation

0 0 0 x'y'z'   m0 x + y + z   M0

0 0 1 x'y'z   m1 x + y + z'   M1

0 1 0 x'yz'   m2 x + y' + z   M2

0 1 1 x'yz   m3 x + y' + z'   M3

1 0 0 xy'z'   m4 x' + y + z   M4

1 0 1 xy'z   m5 x' + y + z'   M5

1 1 0 xyz'   m6 x' + y' + z   M6

1 1 1 xyz   m7 x' + y' + z'   M7

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Eample+ Epress f* as s"m of 

minterms

x y z f1 f2

' ' ' ' '

' ' * * '

' * ' ' '

' * * ' *

* ' ' * '

* ' * ' *

* * ' ' *

* * * * *

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Boolean f"nctions

epressed as #"m of Minterms %#OP& or

Prod"ct of Materms%PO#&are said to be in

Canonical for m .

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EampleEpress the Boolean f"nction $ ( ! - BC in a s"m of 

minterms.

#ol"tion+

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Conversion bet/een Canonical

$orms

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5C Digital 6ogic $amilies116 % 1ransistor 1ransistor 6ogic&

 

116 has an etensive list of digital f"nctions and isc"rrently the most pop"lar logic family. 116s are"s"ally disting"ished by n"merical designation asthe 78'' and 98'' series, some vendors "sedifferent designations s"ch as :''' or ;''' series.

EC6 % Emitter Co"pled 6ogic&

 EC6 is "sed in systems re<"iring high speedoperations. 1he most common EC6 type isdesignated in the *', ''' series. EC6 gate have

three terminals for po/er s"pply. =cc* > =cc? are"s"ally converted to gro"nd and =EE to a 7.? =s"pply.

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MO# %Metal Oide

#emicond"ctor& and 5?6

%5ntegrated 5njection 6ogic&  "sed in circ"its re<"iring high component density.

CMO# %Complementary Metal Oide #emicond"ctor&  are "sed in systems re<"iring lo/ po/er cons"mption.

CMO# circ"it of 8''' series is the common eample.

Positive and @egative 6ogic

a& Positive logic+ %logic * ( high val"e, logic ' ( lo/ val"e.&

b& @egative logic+ %logic ' ( high val"e, logic * ( lo/

val"e.&

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#pecial Characteristics$an A o " t A #pecifies the n"mber of standard loads

that the o"tp"t of a gate can drive /itho"t impairing itsnormal operation. #ometimes the term 3loading4 is"sed instead of fanA o"t.

Po / er Di s si p ation is the s"pplied po/er re<"ired tooperate the gate. 1his is epressed in milli/atts %m&

and represents the act"al po/er dissipated in the gate.

Pro p a g ation D e lay is the average transition delaytime for a signal to propagate from inp"t to o"tp"t/hen the binary signal change val"e. 1he signal

thro"gh a gate take a certain amo"nt of time topropagate from the inp"t to the o"tp"t. 1his interval of time is "s"ally epressed in nanoseconds %n#&.

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#pecial Characteristics

@ o ise Mar g in is the ma. noise voltage added to the

inp"t signal of a digital circ"it that does not ca"se an

"ndesirable change in the circ"it o"tp"t.

@oise "ndesirable signal

*. DC @oise ca"se by drift in the voltage levels.?.  !C @oise random p"lse created by other 

s/itching signals.

@oise margin is epressed in =olts and

represents the maim"m noise signal that can betolerated by the gate.

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#pecial Characteristics

IC Logi !ami"y !#$ %&T o(er ro)agation $oise Margin

Dissi)ation De"ay *n, *-,

*m.,

#tandard 116 *' *' *' '.8

#CO11 116 *' ?? F '.8

6o/ Po/er ?' ? *' '.8

#CO11 116

EC6 ?7 ?7 ? '.?

CMO# 7' '.* ?7 F

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 !ctivity G9