Logic gates r007

Digital Systems
 Introduction to Logic Gates
 Boolean Algebra

Logic Gates
 The building blocks used to create digital circuits are
logic gates
 There are three elementary logic gates and a range
of other simple gates
 Each gate has its own logic symbol which allows
complex functions to be represented by a logic
diagram
 The function of each gate can be represented by a
truth table or using Boolean notation

 The NOT gate (or inverter)

Boolean Algebra
 Boolean Constants
– these are ‘0’ (false) and ‘1’ (true)
 Boolean Variables
– variables that can only take the vales ‘0’ or ‘1’
 Boolean Functions
– each of the logic functions (such as AND, OR and
NOT) are represented by symbols as described above
 Boolean Theorems
– a set of identities and laws – see text for details
9.4

 Boolean identities
AND Function OR Function NOT function
00=0 0+0=0
01=0 0+1=1
10=0 1+0=1
11=1 1+1=1
A0=0 A+0=A
0A=0 0+A=A
A1=A A+1=1
1A=A 1+A=1
AA=A A+A=A
0

 A
A 1

 A
A
1
0 
0
1 
A
A 

Commutative law Absorption law
Distributive law De Morgan’s law
Associative law Note also
 Boolean laws
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Logic gates r007

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