07-04-2012, 01:20 PM
Digital Principles and Logic Design
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INTRODUCTION
One of the fi rst things we have to know is that electronics can be broadly classifi ed
into two groups, viz. analog electronics and digital electronics. Analog electronics
deals with things that are continuous in nature and digital electronics deals with
things that are discrete in nature. But they are very much interlinked. For example, if we
consider a bucket of water, then it is analog in terms of the content i.e., water, but it is
discrete in terms of the container, i.e., bucket. Now though in nature most things are analog,
still we very often require digital concepts. It is because it has some specifi c advantages
over analog, which we will discuss in due course of time.
Many of us are accustomed with the working of electronic amplifi ers. Generally they
are used to amplify electronic signals. Now these signals usually have a continuous value
and hence can take up any value within a given range, and are known as analog signals.
The electronic circuits which are used to process such signals are called analog circuits and
the circuits based on such operation are called analog systems.
NUMBER SYSTEMS
There are several number systems which we normally use, such as decimal, binary, octal,
hexadecimal, etc. Amongst them we are most familiar with the decimal number system. These
systems are classifi ed according to the values of the base of the number system. The number
system having the value of the base as 10 is called a decimal number system, whereas that
with a base of 2 is called a binary number system. Likewise, the number systems having
base 8 and 16 are called octal and hexadecimal number systems respectively.
CONVERSION BETWEEN NUMBER SYSTEMS
It is often required to convert a number in a particular number system to any other
number system, e.g., it may be required to convert a decimal number to binary or octal or
hexadecimal. The reverse is also true, i.e., a binary number may be converted into decimal
and so on. The methods of interconversions are now discussed.
Decimal-to-binary Conversion
Now to convert a number in decimal to a number in binary we have to divide the decimal
number by 2 repeatedly, until the quotient of zero is obtained. This method of repeated
division by 2 is called the ‘double-dabble’ method.
Decimal-to-hexadecimal Conversion
The same steps are repeated to convert a number in decimal to a number in hexadecimal.
Only here we have to divide the decimal number by 16 repeatedly, until the quotient of zero
is obtained. This method of repeated division by 16 is called ‘hex-dabble.’ The remainders
are noted down for each of the division steps.
ANALOG-TO-DIGITAL CONVERTERS
An analog-to-digital converter, or A/D converter, is the reverse system of a D/A converter,
which converts an analog signal to its digital form. In an analog-to-digital converter, the
input analog voltage may have any value in a range and it will produce the digital output
of 2N number of discrete values for an N-bit converter. Therefore, the whole range of analog
voltage is required to be represented suitably in 2N intervals, and each of the intervals
corresponds to a digital output.
[attachment=19700]
INTRODUCTION
One of the fi rst things we have to know is that electronics can be broadly classifi ed
into two groups, viz. analog electronics and digital electronics. Analog electronics
deals with things that are continuous in nature and digital electronics deals with
things that are discrete in nature. But they are very much interlinked. For example, if we
consider a bucket of water, then it is analog in terms of the content i.e., water, but it is
discrete in terms of the container, i.e., bucket. Now though in nature most things are analog,
still we very often require digital concepts. It is because it has some specifi c advantages
over analog, which we will discuss in due course of time.
Many of us are accustomed with the working of electronic amplifi ers. Generally they
are used to amplify electronic signals. Now these signals usually have a continuous value
and hence can take up any value within a given range, and are known as analog signals.
The electronic circuits which are used to process such signals are called analog circuits and
the circuits based on such operation are called analog systems.
NUMBER SYSTEMS
There are several number systems which we normally use, such as decimal, binary, octal,
hexadecimal, etc. Amongst them we are most familiar with the decimal number system. These
systems are classifi ed according to the values of the base of the number system. The number
system having the value of the base as 10 is called a decimal number system, whereas that
with a base of 2 is called a binary number system. Likewise, the number systems having
base 8 and 16 are called octal and hexadecimal number systems respectively.
CONVERSION BETWEEN NUMBER SYSTEMS
It is often required to convert a number in a particular number system to any other
number system, e.g., it may be required to convert a decimal number to binary or octal or
hexadecimal. The reverse is also true, i.e., a binary number may be converted into decimal
and so on. The methods of interconversions are now discussed.
Decimal-to-binary Conversion
Now to convert a number in decimal to a number in binary we have to divide the decimal
number by 2 repeatedly, until the quotient of zero is obtained. This method of repeated
division by 2 is called the ‘double-dabble’ method.
Decimal-to-hexadecimal Conversion
The same steps are repeated to convert a number in decimal to a number in hexadecimal.
Only here we have to divide the decimal number by 16 repeatedly, until the quotient of zero
is obtained. This method of repeated division by 16 is called ‘hex-dabble.’ The remainders
are noted down for each of the division steps.
ANALOG-TO-DIGITAL CONVERTERS
An analog-to-digital converter, or A/D converter, is the reverse system of a D/A converter,
which converts an analog signal to its digital form. In an analog-to-digital converter, the
input analog voltage may have any value in a range and it will produce the digital output
of 2N number of discrete values for an N-bit converter. Therefore, the whole range of analog
voltage is required to be represented suitably in 2N intervals, and each of the intervals
corresponds to a digital output.