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

5.3 Logic 183
C
D
C
D
(a)
(b)
C
D
C
D
(c)
(d)
(e)
C
D
FigureS.13
8 SeeFigure S.13.
10 (a)Function
(b)Not afunction since 0 is mapped to two elements
(c)Not afunction since 2 is notmapped to anything
11 r isnot afunction because 1 is notmapped to
anything.
5.3 LOGIC
In Section 5.4 we will examine Boolean algebra. This concerns itself with the manipulation
of logic statements and so is suitable for analysing digital logic circuits. In this
section we introduce the basic concepts of logic by means of logic gates as these form
the usual startingpoint for engineers studying this topic.
5.3.1 TheORgate
The OR gate is an electronic device which receives two inputs each in the form of a
binary digit, that is 0 or 1, and produces a binary digit as output, depending upon the
values of the two inputs.Itisrepresented by the symbolshown inFigure 5.5.
AandBarethetwoinputs,andF isthesingleoutput.Ashigh(1)orlow(0)voltages
are applied to A and B various possible outputs are achieved, these being defined by
means of a truth table as shown in Table 5.3. So, for example, if a low (0) voltage is
applied to A and a high (1) voltage is applied to B, the output is a high (1) voltage at
F. We note that a ‘1’ appears in the right-hand column of the truth table whenever A
orBtakes the value 1,hence the name OR gate. We use the symbol + torepresent OR.
BecauseitconnectsthevariablesAandB,ORisknownasalogicalconnective.Weshall
meet other logical connectives shortly. This connective is also known as adisjunction,
so thatA +Bissaidtobethe disjunction ofAandB.
Table5.3
The truth table for an OR gate
with inputsAandB.
A
B
Figure5.5
Symbol foran ORgate.
F = A + B
A B F=A+B
1 1 1
1 0 1
0 1 1
0 0 0