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

184 Chapter 5 Discrete mathematics
Table5.4
ThetruthtableforanANDgate
with inputsAandB.
A
B
Figure5.6
Symbol foran AND gate.
F = A . B
A B F=A·B
1 1 1
1 0 0
0 1 0
0 0 0
Table5.5
The truth table for
a NOTgate.
A
F = A
A
F=A
Figure5.7
Symbol foran inverter.
1 0
0 1
5.3.2 TheANDgate
It is possible to construct another electronic device called an AND gate which works
in a similar way except that the output only takes the value 1 when both inputs are 1.
ThesymbolforthisgateisshowninFigure5.6andthecompletetruthtableisshownin
Table 5.4. The logical connective AND is given the symbol · and is known as a conjunctionso
thatA·Bissaidtobethe conjunctionofAandB.
5.3.3 TheinverterorNOTgate
The inverter is a device with one input and one output and has the symbol shown in
Figure 5.7. It has a truth table defined by Table 5.5. If the input isA, then the output is
representedby the symbolA, known as the complement ofA.
5.3.4 TheNORgate
This gate is logically equivalent to a NOT gate in series with an OR gate as shown in
Figure 5.8. It is represented by the symbol shown in Figure 5.9 and has its truth table
defined inTable 5.6.
A
B
A + B
Figure5.8
A NOTgatein series with an OR gate.
A
B
Figure5.9
Symbol foraNOR gate.
F = A + B
F = A + B
Table5.6
ThetruthtableforaNORgate.
A B F =A +B
1 1 0
1 0 0
0 1 0
0 0 1