Logi

cGat
es
2

I
NTRODUCTI
ON
Alogicgateisanel ementarybuil
dingbl ockofa 
digi
tal
 ci
rcui
t.I
tmakes
“l
ogicaldeci
sions”basedont hedifferentcombinati
onsofdigit
alsignal
s
presentonitsinputs.Di
git
allogi
cgat esmayhav emorethanonei nput
butgenerall
yonlyhav eonedigit
aloutput .Mostl
ogicgateshavetwo
i
nput sandoneout put.

Knowl
edgeCl
oud

Agateisadigi
talci
rcuitt
hatisdesi
gnedf orper
formanceapar t
icul
ar
l
ogical
operati
on.Asitworksaccordingtosomel ogical
rel
ati
onship
bet
weeninputandout putvol
tages,
soi ti
sgenerall
yknownas“ LOGIC
GATES”

Atanygi v
enmoment ,everyterminali
sinoneoft hetwo bi
nary
condit
ions l
ow (0)or
 high (
1),repr
esentedbydif fer
entvolt
agelevel
s.
Thelogicstateofatermi nalcan,andgenerall
ydoes, changeoften,as
thecir
cuitprocessesdata.Inmostl ogi
cgat es,thelowstatei
s
approximatelyzerovol
ts( 0V),whil
ethehighst ateisapproxi
mat el
yfi
ve
volt
spositive(+5V).
I
ndividuallogicgatescanbeconnect edt ogethertof orm combi nati
onal
orsequent ial
circui
tsorlargerlogicgat efuncti
ons.Di ff
erenttypesof
l
ogicgat eimpl ementsdiffer
entBool eanf uncti
on,thatis,itperf
or msa
l
ogical operati
onononeormor elogici nputsandpr oducesasi nglelogi
c
output.Dependi ngont hecontext,theterm mayr efert oanideal l
ogic
gate,onet hathasforinstancezer oriset i
meandunl imit
edf an-out,
orit
mayr efertoanon- idealphysi
cal device.

Logicgat esareprimari
lyi
mpl ementedel ect
roni
callyusi
ngdi
odesor
tr
ansistors,butcanalsobeconstructedusi ngelectr
omagnet
icrel
ays
(r
elaylogic),f
lui
diclogi
c,pneumaticlogic,opti
cs,molecul
es,
oreven
mechani calelements.Wit
hampl i
fi
cat i
on, l
ogicgatescanbecascadedi
n
3 thesamewayt hatBool
eanfunct
ionscanbecomposed, al
l
owingthe
constr
uctionofaphy si
cal
modelofallofBool
eanlogi
c,andther
efore,
all
ofthealgori
thmsandmat hemati
csthatcanbedescri
bedwi t
hBoolean
l
ogic.

Alargenumberofelect
roni
ccircui
ts(i
ncomput ers,controluni
ts,
andso
on)aremadeupofl ogi
cgates.Theseprocesssignalsrepresentei
ther
tr
ueorfalse.Themostcommonsy mbolsusedtor epresentlogi
cgates
areshownbel ow.
4 1.NORgat
e:

TheNORgat eisadi gi
tall
ogicgat ewhi chbehav esaccor dingt o
thetr
ut ht
able.AHI GHout put( 1)result
sifbot htheinput stothe
gateareLOW ( 0) ;
ifoneorbot hinputisHI GH( 1),aLOW out put( 0)
resul
ts.NORi st heresultofthenegat i
onoft heORoper ator.Itcan
alsobeseenasanANDgat ewi thalltheinputsinverted.NORi sa
funct
ionall
ycompl eteoperation—NORgat escanbecombi nedt o
generateanyot herlogicalfunction.Bycont rast,
theORoper at oris
monot oni
casi tcanonl ychangeLOW t oHI GHbutnotv icev ersa.

Wewil
lst
artwi
tha2inputNORgat
e.Thesy
mbol
fora2i
nput
NORgat
eisasf
oll
ows.(
Nextpage)

A
Q
B

Thet
rut
htabl
efort
he2i
nputNORgat
eisshownbel
ow.

I
nput
s Out
put

B A Q

0 0 1

0 1 0

1 0 0
TheBool
ean expr
essi
onf
ora2
1 1 0
i
nputNORgatei
s
5

Summar
yof2-
inputLogi
cGat
es
Thefol
lowingTrut
hTabl
ecompar
est
hel
ogi
calf
unct
ionsoft
he2-
input
l
ogicgatesabov
e.

I
nput
s Tr
uthTabl
eOut
put
sForEachGat
e

A B AND NAND OR NOR EX-

0 0 0 1 0 1 0 1

0 1 0 1 1 0 1 0

1 0 0 1 1 0 1 0

1 1 1 0 1 0 0 1

Thefol
l
owingtabl
egiv
esalistoft
hecommonl
ogi
cfunct
ionsandt
hei
r
equi
val
entBool
eannot
ati
on.

Logi
cFunct
ion Bool
eanNot
ati
on

AND A.
B

OR A+B

NOT A

NAND A.
B

NOR A+B

EX-
OR (
A.B)
 + 
(A.  
B)orA  
  
B

EX-
NOR (
A.B)
 + or
   
A  
  
B
6

Resul
t
Wehadmainlydi
scussedaboutt
hedesi
gn,
proper
tyandoper
ati
onof
var
iousl
ogi
cgates

Usingcombinati
onsoflogicgat
es,compl exoperati
onscanbe
perfor
med.Intheor
y,t
her ei
snolimittothenumberofgat esthatcanbe
arr
angedtogetheri
nasi ngl
edevi
ce.Butinpr act
ice,thereisalimi
ttothe
numberofgatesthatcanbepackedi ntoagivenphy sicalspace.

Arraysoflogi
cgat esaref
oundi ndigit
alintegrat
edcir
cui
ts(ICs)
.AsI C
technologyadvances,t
herequiredphy si
cal vol
umeforeachindi
vidual
l
ogi cgatedecreasesanddigit
aldevicesoft hesameorsmal l
ersize
becomecapabl eofperfor
mi ngever-more-compl i
cat
edoperati
onsat
ever-i
ncreasi
ngspeeds.
7