082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

192 Chapter 5 Discrete mathematics
This is the expression for an exclusive OR gate with inputsC1 andX. It is therefore
possible to obtainS2 with two exclusive OR gates which are usually available
asabasicbuildingblockonanintegratedcircuit.ThecircuitforS2isshowninFigure
5.17. Turning toC2, wehave
C2 =C1·A2·B2+C1·A2·B2+C1·A2·B2+C1·A2·B2
=A2·B2·(C1+C1)+C1·(A2·B2+A2·B2)
=A2·B2 +C1·X
by the complement law
by the distributive law
sinceC1 +C1 = 1, whereX is given by Equation (5.3). The output,X, has already
been generated to produceS2 but can be used again provided the exclusive OR gate
can stand feeding two inputs. Assuming this is so then the final circuit for the fulladder
isshown inFigure 5.18.
A2
B2
X
C1
S2
Figure5.17
Circuit to implementS2 =C1·X +C1·X,
whereX =A2 ·B2 +A2 ·B2.
A2
B2
C1
X
S2
A2 . B2
C1 . X
C2
Figure5.18
Circuit to implement the stage 2 full-adder.
Engineeringapplication5.4
Realizationoflogicgates
Logic gates are usually constructed from one or more transistors. The most commontechnologyusedisCMOS(complementarymetal-oxidesemiconductor)logic,
which was invented by Frank Wanlass and was perfected whilst he was working
at Fairchild Semiconductor in the 1960s. CMOS logic makes use of two different
typesoftransistorknownasPMOS(p-typemetal-oxidesemiconductor)andNMOS
(n-type metal-oxide semiconductor) transistors. Both types can be readily manufactured
in vast numbers on a single silicon wafer along with their associated wiring.
Thisprincipleistheconstructionalbasisofmodernmicroprocessorswhichmaycontainbillionsofindividualtransistors.Thetermvery-large-scaleintegration(VLSI)
was coined to refer to the practice of assembling such a large number of transistor
devices onasinglesilicon wafer.
Figure5.19showstheconstructionofasingleNANDgatemadefromitsindividual
transistors.