This document discusses digital systems and logic gates. It introduces logic gates as the building blocks of digital circuits, describing the AND, OR, NOT, NAND and NOR gates. It also covers Boolean algebra, including Boolean constants, variables, functions and theorems. Boolean algebra defines the identities and laws for AND, OR and NOT logic functions using symbolic notation.

1. Digital Systems
 Introduction to Logic Gates
 Boolean Algebra

2. 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

3.  The AND gate

4.  The OR gate

5.  The NOT gate (or inverter)

6.  A logic buffer gate

7.  The NAND gate

8.  The NOR gate

9.  The Exclusive OR gate

10.  The Exclusive NOR gate

11. 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

12.  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 

13. Commutative law Absorption law
Distributive law De Morgan’s law
Associative law Note also
 Boolean laws
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