Download Digital Systems: Introduction to Binary Quantities, Logic Gates, and Boolean Algebra and more Exercises Basic Electronics in PDF only on Docsity!
Digital Systems
Introduction
Binary Quantities and Variables
Logic Gates
Boolean Algebra
Combinational Logic
Number Systems and Binary Arithmetic
Numeric and Alphabetic Codes
Chapter 9
Introduction
Digital systems are concerned with digital signals
Digital signals can take many forms
Here we will concentrate on binary signals since
these are the most common form of digital signals
– can be used individually
perhaps to represent a single binary quantity or the state of a
single switch
– can be used in combination
to represent more complex quantities
(^) A binary arrangement with two switches in series
L = S1 AND S
(^) A binary arrangement with two switches in parallel
L = S1 OR S
(^) Three switches in parallel
L = S1 OR S2 OR S
(^) A series/parallel arrangement
L = S1 AND ( S2 OR S3 )
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 AND gate
(^) The NOT gate (or inverter)
(^) A logic buffer gate
(^) The NOR gate
(^) The Exclusive OR gate
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
(^) Boolean identities AND Function OR Function NOT function 0 0=0 0+0= 0 1=0 0+1= 1 0=0 1+0= 1 1=1 1+1= A 0=0 A +0= A 0 A =0 0+ A = A A 1= A A +1= 1 A = A 1+ A = A A = A A + A = A A A 0 A A 1
A A
