66856 Digital Electronics & Microprocessors T P C
2 3 3
OBJECTIVES
Upon completion
of this content, students will be able to achieve and acquire knowledge, skills
and attitude in the area of Digital Electronics and Microprocessors special
emphasis on:
Number system, Binary arithmetic, and codes
Logic gates and Sequential logic circuits
Semiconductor memories, A/D and D/A converters
Microprocessors
SHORT
DESCRIPTION
Basic Digital
Circuits; Numbers systems and codes; Combinational logic circuits; Flip-flops
and shift registers; Counters; A/D and D/A converters; Semiconductor memories;
8085, 8086 microprocessors.
DETAILS
DECEPTION
Theory:
1. Understand
Number systems and codes.
1.1 Describe binary, octal and
Hexadecimal Number systems.
Numbers Representation
Systems – Decimal, Binary, Octal, and Hexadecimal
In this article, we’ll
discuss different number representation systems, where they are used and
why they are useful. Briefly, we’ll go through decimal, binary, octal
and hexadecimal number representation.
Decimal (base 10)
The most common system
for number representation is the decimal. Everybody is using it. It’s so
common that most people must believe that is the only one. It’s used in
finances, engineering, and biology, almost everywhere we see and
use numbers.
If someone is asking you
to think at a number for sure you’ll think at a decimal number. If you think of
a binary or hexadecimal one, you must have an extreme passion for arithmetic or
software/programming.
As the name is saying the decimal number system is using 10
symbols/characters. In the Latin language, 10 is “decem” so decimal might be linked
to the Latin word.
|
Decimal Symbols |
|||||||||
|
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
As you can see there are
10 symbols from 0 to 9. With these symbols, we can construct all the numbers in the
decimal system.
All the numbers in the decimal system can be constructed by
using the above-mentioned symbols (0 … 9) multiplied with the power of 10. The power
of ten gives us ones, tens, hundreds, thousands, and so on.
|
10 k |
… |
10 5 |
10 4 |
10 3 |
10 2 |
10 1 |
10 0 |
|
N |
… |
100000 |
10000 |
1000 |
100 |
10 |
1 |
The example below breaks down the decimal number 67049 into powers of 10
multiplied with numbers between 0 and 9. This is just to show that any number in the
decimal system can be decomposed into a sum of terms made off from the product
of the power of 10 and the symbols 0 … 9.
|
67049 |
|||||||
|
10 7 |
10 6 |
10 5 |
10 4 |
10 3 |
10 2 |
10 1 |
10 0 |
|
0 |
0 |
0 |
6 |
7 |
0 |
4 |
9 |
|
67049 =6⋅10 4 =60000 +7⋅10 3 +7000 +0⋅10 2 +0 +4⋅10 1 +40 +9⋅10 0 +9 |
|||||||
The same technique is
going to be applied to the binary, octal and hexadecimal systems, is in fact
a method of converting a number from the decimal system in another format (base).
We can keep in mind these
characteristics of the decimal numbers system:
- it’s
using 10 symbols
- can
be decomposed in factors containing powers of 10
- it’s
the most common number representation system
Binary (base 2)
Let’s step into the geek
side now.
Another number representation system is the binary one.
As the name suggests and by analogy, with the decimal system we can say that the binary system is using only 2 symbols/characters:
|
Binary Symbols |
|
|
0 |
1 |
In the binary representation, we only use 0 (zeros) and 1 (ones) to represent numbers.
The binary system is used
wherever you want to store information in electronic format. All the computers
that you know, intelligent devices, everything that has to do with electronics, and microcontrollers use the binary system.
In electronics (digital)
all the operations are done using two levels of voltage: high and low. Each
level of voltage is assigned to a value/symbol: HIGH for 1 and LOW for 0. For a
microcontroller that is supplied with +5V the 1 (high) will be
represented by +5 V and the 0 (low) by 0 V.
Roughly we can say that
the binary system is used because it can be translated into an electronic signal.
All the decimal numbers we can think of can be represented in
binary symbols. We do this by using a sum between terms of the power of 2
multiplied with 0 or 1.
|
2 k |
… |
2 7 |
2 6 |
2 5 |
2 4 |
2 3 |
2 2 |
2 1 |
2 0 |
|
N |
… |
128 |
64 |
32 |
16 |
8 |
4 |
2 |
1 |
For example, we’ll use the number 149 (decimal representation)
and transform it into a binary representation. We could use any number but if
it’s too big it would end up into a long string of zeros and ones.
|
149 |
|||||||
|
2 7 |
2 6 |
2 5 |
2 4 |
2 3 |
2 2 |
2 1 |
2 0 |
|
1 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
|
149 =1⋅2 7 =128 +0⋅2 6 +0 +0⋅2 5 +0 +1⋅2 4 +16 +0⋅2 3 +0 +1⋅2 2 +4 +0⋅2 1 +0 +1⋅2 0 +1 |
|||||||
As you can see the
decimal number 149 is represented in the binary system by a series of zeros and ones (10010101). Usually to distinguish
between decimal or binary numbers, we must specify the base to which we are
referring to. The base is described as a subscript after the last character of
the number
Example:
|
Decimal (base 10) |
Binary (base 2) |
|
149 10 |
10010101 2 |
By specifying the base of the number we eliminate the
probability of confusion, because the same representation (e.g. 11) can mean
different things for different bases.
|
11 2 ≠11 10 |
Another way to avoid
confusion is to use a special notation (prefix) for binary numbers. This is
because 1100 can represent eleven
hundreds in a decimal system or the decimal twelve represented in binary
system. So if want to specify a binary number we use the prefix 0b. Example: 0b1100.
Briefly the
characteristics of a binary system are:
- it’s
using 2 symbols
- can
be decomposed in factors containing powers of 2
- it’s
used in computers, microcontrollers
Octal (base 8)
All the numbers in the octal of the system are represented using 8 symbols/characters, from 0 to 7. The reason for using the octal system instead of the decimal one can be various. One of them is that
instead of using our fingers for counting, we use the spaces between fingers.
Humans have 4 spaces between the fingers of one hand; in total
we’ll have 8 spaces, for both hands. In this case, it makes sense to use an
octal number representation system instead of a decimal one. The drawback is
that higher numbers will require more characters compared to the decimal one.
|
Octal Symbols |
|||||||
|
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
To transform a decimal represented number into an octal system
we split it into terms containing the power of 8:
|
8 k |
… |
8 5 |
8 4 |
8 3 |
8 2 |
8 1 |
8 0 |
|
N |
… |
32768 |
4096 |
512 |
64 |
8 |
1 |
As an example we are going to represent the decimal number 67049 in octal base:
|
67049 |
|||||
|
8 5 |
8 4 |
8 3 |
8 2 |
8 1 |
8 0 |
|
2 |
0 |
2 |
7 |
5 |
1 |
|
67049 =2⋅8 5 =65535 +0⋅8 4 +0 +2⋅8 3 +1024 +7⋅8 2 +448 +5⋅8 1 +40 +1⋅8 0 +1 |
|||||
Hexadecimal (base 16)
The hexadecimal number representation system is using 16
symbols/characters to define numbers. It’s used in computer
science mostly because can represent bigger decimal numbers with fewer
characters.
|
Hexadecimal Symbols |
|||||||||||||||
|
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
A |
B |
C |
D |
E |
F |
Compared with the decimal system it’s also using numeric symbols
from 0 to 9. Additionally, it’s using alphanumeric characters from A to F for
values between 10 and 15.
|
16 k |
… |
16 5 |
16 4 |
16 3 |
16 2 |
16 1 |
16 0 |
|
N |
… |
1048576 |
65535 |
4096 |
256 |
16 |
1 |
To represent a decimal number in the hexadecimal format we split the
decimal number into a sum of terms. Each term is a product between a
hexadecimal symbol and a power of 16.
|
67049 |
||||
|
16 4 |
16 3 |
16 2 |
16 1 |
16 0 |
|
1 |
0 |
5 |
E |
9 |
|
67049 =1⋅16 4 =65536 +0⋅16 3 +0 +5⋅16 2 +1280 +E⋅16 1 +224 +9⋅16 0 +9 |
||||
The representation of the
decimal number 67049 in hexadecimal format as 105E9. Similar to the binary system a common
practice is to use the prefix “0x” to distinguish from the decimal
notation. Example: 0x105E9.
Briefly the
characteristics of a hexadecimal number representation system are:
- it’s
using 16 symbols
- can
be decomposed in factors containing powers of 16
- it’s
used in computers, microcontrollers
The table below summaries the characteristics of the above
mentioned number representation systems.
|
System |
Number of Symbols |
Symbols |
Prefix |
Example |
|
Decimal |
10 |
0, 1, 2, 3, 4, 5, 6, 7, 8, 9 |
None |
147 |
|
Binary |
2 |
0, 1 |
0b |
0b10010011 |
|
Hexadecimal |
16 |
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A,B, C, D, E, F |
0x |
0x93 |
Both the octal and hexadecimal number representation systems are
linked to the computer system, mainly with the kind of processors and
microcontrollers. For example, if the microprocessor is using 8-bit data then
the octal system is suitable to interface data. If the microprocessor is on 16
bits then the hexadecimal system is appropriate to represent data
1.2 Convert one number system to another.
Number System Conversion
As we know, the number system is a form of expressing numbers. In number system conversion, we will study to convert several one base, to a number of another base. There are a variety of number systems such as binary numbers, decimal numbers, hexadecimal numbers, octal numbers, which can be exercised.
In this
article, you will learn the conversion of one base number to another base
number considering all the base numbers such as decimal, binary, octal and
hexadecimal with the help of examples. Here, the following number system
conversion methods are explained.
·
Binary to Decimal Number System
·
Decimal to Binary Number System
·
Octal to Binary Number System
·
Binary to Octal Number System
·
Binary to Hexadecimal Number System
·
Hexadecimal to Binary Number System
Get the pdf of a number system with a brief description in it. The general representation of
number systems are;
Decimal Number
– Base 10 = N10
Binary Number –
Base 2 =N2
Octal Number –
Base 8 = N8
Hexadecimal
Number – Base 16 =N16
Number System
Conversion Table
|
Binary Numbers |
Octal Numbers |
Decimal Numbers |
|
Hexadecimal Numbers |
|
0000 |
0 |
0 |
|
0 |
|
0001 |
1 |
1 |
|
1 |
|
0010 |
2 |
2 |
|
2 |
|
0011 |
3 |
3 |
|
3 |
|
0100 |
4 |
4 |
|
4 |
|
0101 |
5 |
5 |
|
5 |
|
0110 |
6 |
6 |
|
6 |
|
0111 |
7 |
7 |
|
7 |
|
1000 |
10 |
8 |
|
8 |
|
1001 |
11 |
9 |
|
9 |
|
1010 |
12 |
10 |
|
A |
|
1011 |
13 |
11 |
|
B |
|
1100 |
14 |
12 |
|
C |
|
1101 |
15 |
13 |
|
D |
|
1110 |
16 |
14 |
|
E |
|
1111 |
17 |
15 |
|
F |
Number System
Conversion Methods
Number system
conversions deal with the operations to change the base of the numbers. For
example, to change a decimal number with base 10 to a binary number with base 2.
We can also perform arithmetic operations like addition, subtraction,
multiplication on the number system. Here, we will learn the methods to convert
the number of one base to the number of another base starting with the decimal
number system. The representation of number system base conversion in general
form for any base number is;
(Number)b
= dn-1 dn-2—–.d1 d0 . d-1
d-2 —- d-m
In the above
expression, dn-1 dn-2—–.d1 d0 represents
the value of integer part and d-1 d-2 —- d-m
represents the fractional part.
Also, dn-1
is the Most significant bit (MSB) and d-m is the Least
significant bit (LSB).
Now let us
learn, conversion from one base to another.
|
|
|
|
|
|
|
|
|
Decimal to
Other Bases
Converting a
decimal number to other base numbers is easy. We have to divide the decimal
number by the converted value of the new base.
Decimal to Binary
Number:
,
Suppose if we have to convert decimal to binary, then
divide the decimal number by 2
Example 1. Convert (25)10 to
binary number.
Solution: Let us create a table based on
this question.
|
Operation |
Output |
Remainder |
|
25 ÷ 2 |
12 |
1(MSB) |
|
12 ÷ 2` |
6 |
0 |
|
6 ÷ 2 |
3 |
0 |
|
3 ÷ 2 |
1 |
1 |
|
1 ÷ 2 |
0 |
1(LSB) |
Therefore, from
the above table, we can write,
(25)10 =
(11001)2 completed on
19/8/21.
Decimal to
Octal Number: next class on 22/8/21.
To convert decimal
to the octal number we have to divide the given original number by 8
such that base 10 changes to base 8. Let us understand with the help of an
example.
Example 2:
Convert 12810 to octal number.
Solution: Let
us represent the conversion in tabular form.
|
Operation |
Output |
Remainder |
|
128÷8 |
16 |
0(LSB) |
|
16÷8 |
2 |
0 |
|
2÷8 |
0 |
2(MSB) |
Therefore, the
equivalent octal number = 2008
Decimal to
Hexadecimal:
Again in decimal to hex
conversion, we have to divide the given decimal number by 16.
Example 3:
Convert 12810 to hex.
Solution: As
per the method, we can create a table;
|
Operation |
Output |
Remainder |
|
128÷16 |
8 |
0(MSB) |
|
8÷16 |
0 |
8(LSB) |
Therefore, the
equivalent hexadecimal number is 8016
Here MSB stands
for a Most significant bit and LSB stands for a least significant bit.
Other Base
System to Decimal Conversion
Binary to
Decimal:
In this
conversion, binary number to a decimal number, we use multiplication method, in
such a way that, if a number with base n has to be converted into a number with
base 10, then each digit of the given number is multiplied from MSB to LSB with
reducing the power of the base. Let us understand this conversion with the help
of an example.
Example 1. Convert (1101)2 into
a decimal number.
Solution: Given a binary number (1101)2.
Now, multiplying
each digit from MSB to LSB with reducing the power of the base number 2.
1 × 23
+ 1 × 22 + 0 × 21 + 1 × 20
= 8 + 4 + 0 + 1
= 13
Therefore,
(1101)2 = (13)10
Octal to
Decimal:
To convert
octal to decimal, we multiply the digits of octal number with decreasing power
of the base number 8, starting from MSB to LSB and then add them all together.
Example 2:
Convert 228 to decimal numbers.
Solution:
Given, 228
2 x 81
+ 2 x 80
= 16 + 2
= 18
Therefore, 228 =
1810
Hexadecimal to
Decimal:
Example 3:
Convert 12116 to decimal number.
Solution: 1 x
162 + 2 x 161 + 1 x 160
= 16 x 16 + 2 x
16 + 1 x 1
= 289
Therefore, 12116
= 28910
Hexadecimal to
Binary Shortcut Method
To convert
hexadecimal numbers to binary and vice versa are easy, you just have to memorize
the table is given below.
|
Hexadecimal Number |
Binary |
|
0 |
0000 |
|
1 |
0001 |
|
2 |
0010 |
|
3 |
0011 |
|
4 |
0100 |
|
5 |
0101 |
|
6 |
0110 |
|
7 |
0111 |
|
8 |
1000 |
|
9 |
1001 |
|
A |
1010 |
|
B |
1011 |
|
C |
1100 |
|
D |
1101 |
|
E |
1110 |
|
F |
1111 |
You can easily
solve the problems based on hexadecimal and binary conversions with the help of
this table. Let us take an example.
Example: Convert (89)16 into
a binary number.
Solution: From the table, we can get the binary value of 8 and 9, hexadecimal base numbers.
8 = 1000 and 9
= 1001
Therefore, (89)16
= (10001001)2
Octal to Binary
Shortcut Method
To convert octal to binary
number, we can simply use the table. Just like having a table for hexadecimal
and its equivalent binary, in the same way, we have a table for octal and its
equivalent binary number.
|
Octal Number |
Binary |
|
0 |
000 |
|
1 |
001 |
|
2 |
010 |
|
3 |
011 |
|
4 |
100 |
|
5 |
101 |
|
6 |
110 |
|
7 |
111 |
Example: Convert (214)8 into
a binary number.
Solution: From
the table, we know,
2 → 010
1 → 001
4 → 100
Therefore,(214)8
= (010001100)2
Practice Problems
on Number System Conversion
1. Convert 14610 into a
binary number system
2. Convert 1A716
into the decimal number system
3. Convert (110010)2 into
octal number system
4. Convert DA216 into the
binary number system
5. Convert 46528 into
the binary number system
Frequently Asked
Question on the Number System Conversion
Why do we need
the number system conversion?
One of the most
important applications of the number system is in computer technology.
Generally, a computer uses the binary number system, but humans will use the
hexadecimal number system, as it is easier to understand. For this reason, the
number system conversion is required.
What is meant
by the base 2 number system?
The base 2 the number system is called the binary number system. It uses only two digits, such
as 0, 1. For example, the number 6 is represented by 0110 (or) 110.
Write down the
conversion procedure from decimal to binary number system?
The steps to
convert the decimal number system to binary number system are:
Divide the given number by 2
Now, use the obtained quotient for the next iteration
Obtain the remainder for the binary number
Repeat the steps until the quotient is equal to 0
What is meant
by the base 8 number system?
The base 8 number system is called the octal number system. It uses the digits such as 0,
1, 2, 3, 4, 5, 6, 7.
What is meant
by the hexadecimal number system?
The hexadecimal number system is called the base 16 number system. It uses the digits from 0 to
9, and A, B, C, D, E, F
1.3 Compute binary, Octal, and hexadecimal
arithmetic.
Convert Hexadecimal To Octal
In the number
system, we come across four different types of the number system, i.e.
hexadecimal, octal, decimal, and binary. The conversion of these numbers from
one form to another is possible. To convert hexadecimal to octal
numbers, we need to convert hexadecimal to its equivalent decimal number first
and then decimal to octal. Before this conversion, first,
go through the basic definition of hexadecimal and octal numbers.
What Are
Hexadecimal Numbers?
Hexadecimal
numbers are the numbers which have base 16. It uses 16 different digits
to represent the numbers. It is denoted as h16, where h is a hexadecimal number. It may be a
combination of alphabets and numbers. Thus, it includes numbers from 0 to 9 and
alphabets A to F.
Example: (AB2)16, (98D1)16, (AFD)16
What are Octal
Numbers?
Octal numbers have base 8. These numbers use
digits from 0 to 7, total 8 digits and hence, they are called octal number
systems. Octal numbers have base 8. It is denoted as o8 and o is an octal number. It
does not use digits 8 and 9 to represent a number.
Example: (112)8, (275)8,(45)8
Hexadecimal to
Octal Conversion
Conversion of
hexadecimal to octal cannot be done directly. Firstly we need to convert
hexadecimal into its equivalent decimal number then decimal to octal. Follow
the steps below to understand the process.
·
Consider the given hexadecimal number
·
First count the number of digits in the number
·
If n is the position of the digit from the right end then
multiply each digit with 16n-1
·
Add the terms after multiplication
·
Resultant is the equivalent decimal form
·
Divide the decimal number with 8
·
Note down the remainder
·
Repeat the previous two steps with the quotient, until the
quotient is zero
·
Write the remainders in reverse order
·
The obtained number is the required result
Another Method
to Convert Hex to Octal
There is
another method to convert any hexadecimal to its equivalent octal. As we know,
hexadecimal numbers include binary digits; therefore, we can club these binary
numbers into a pair so that we can relate it with the octal numbers. Let us
check the method with steps and examples:
·
For each given hexadecimal number digit, write the equivalent
binary number. If any of the binary equivalents are less than 4 digits, add 0’s
to the left side.
·
Combine and make the groups of binary digits from right to left,
each containing 3 digits. Add 0’s to the left if there are less than 3 digits
in the last group.
·
Find the octal equivalent of each binary group.
Let us see an
example here:
Example:
Convert 1BC16 into an octal number.
Solution:
Given, 1BC16 is a hexadecimal number.
1 → 0001,
B → 1011, C →1100
Now group them
from right to left, each having 3 digits.
000, 110, 111,
100
000→0,
110 →6, 111→7, 100→4
Hence, 1BC16 = 6748
Hex to Octal
Conversion Table
|
Hexadecimal |
Octal |
Equivalent Decimal |
Equivalent Binary |
|
0 |
0 |
0 |
0 |
|
1 |
1 |
1 |
1 |
|
2 |
2 |
2 |
10 |
|
3 |
3 |
3 |
11 |
|
4 |
4 |
4 |
100 |
|
5 |
5 |
5 |
101 |
|
6 |
6 |
6 |
110 |
|
7 |
7 |
7 |
111 |
|
8 |
10 |
8 |
1000 |
|
9 |
11 |
9 |
1001 |
|
A |
12 |
10 |
1010 |
|
B |
13 |
11 |
1011 |
|
C |
14 |
12 |
1100 |
|
D |
15 |
13 |
1101 |
|
E |
16 |
14 |
1110 |
|
F |
17 |
15 |
1111 |
Hexadecimal to
Octal Questions
Q.1: Find the
equivalent octal form of C116.
Solution:
Given, a hexadecimal number is C1
C116 = (C × 161) + (1 × 160)
= C × 16 + 1 ×
1
=12 × 16 + 1
= 192 + 1
C116 =193 (Decimal form)
Now we have to
convert this decimal to octal number;
The octal
number is 3018
Hence, C116 = 3018
Q.2: Find the
equivalent octal form of F16.
Solution:
Given, a hexadecimal number is F.
F16 = (F × 160)
= F × 1
= F
= 15(Decimal
form)
Now we have to
convert this decimal to equivalent octal number;
The octal
number is 178
Hence, F16 = 178
Q.3: Find the
equivalent octal form of 10516
Solution: Given, a hexadecimal number is
105.
10516 = (1 × 162) + (0 × 161) + (5 × 160)
= 1×256 + 0 ×
16 + 5 × 1
=256 + 0 +5
= 261(Decimal
form)
Now we have to
convert this decimal to equivalent octal;
The octal
number is 4058
Hence, 10516 = 4058
Practice
Questions
1. Convert ABCD16 to equivalent octal form.
2. Convert 91216 to equivalent octal form.
3. Convert 216 to equivalent octal form.
4. Convert 1016 to equivalent octal form
1.4 Describe BCD Code, Excess- 3 Code,
Gray Code, Alphanumeric Codes.
BCD (binary-coded
decimal), also called alphanumeric BCD, alphameric BCD, BCD Interchange Code,
or BCDIC is a family of representations of numerals, uppercase Latin letters,
and some special and control characters as six-bit character codes.
What is the BCD code
excess-3 code and gray code?
Excess-3 Code is a non-weighted
BCD (8421) Code. Excess-3 Code is derived from 8421 code by adding 0011 (3)
to all code groups. It is a sequential code, thus can be also used for
performing arithmetic operations.
...
Excess-3 Code.
|
Decimal Numbers |
Binary Numbers |
Excess-3 Code (Binary Number + 0011) |
|
8 |
1000 |
1011 |
|
9 |
1001 |
1100 |
What are BCD and GREY
code?
Binary Coded Decimal
(BCD) is a way to store the decimal numbers in binary form. The number
representation requires 4 bits to store every decimal digit (from 0 to 9).
Since there are 10 different combinations of BCD, we need at least a 4-bit Gray
Code to create a sufficient number of these combinations.
Different Types of
Binary Codes | BCD (8421), 2421, Excess-3, Gray
·
Binary Weights.
·
8421 Code or BCD Code.
·
2421 Code.
·
5211 Code.
·
Reflective Code.
·
Sequential Codes.
How do I find my BCD
code?
Simply divide the
binary number into groups of four digits, starting with the least
significant digit, and then write the decimal digit represented by each 4-bit
group. Add additional zero's at the end if required to produce a complete 4-bit
grouping. So for example, 1101012 would become: 0011 01012
or 3510 in decimal.
How do I change my BCD
code from excess-3?
Excess-3 to BCD
conversion
The BCD code can be calculated by subtracting 3, i.e., 0011 from each
four-digit Excess-3 code.
What is Gray code
example?
Gray Code system is a
binary number system in which every successive pair of numbers differs in only one
bit. ... For example, the states of a system may change from 3(011) to
4(100) as- 011 — 001 — 101 — 100.
Where is GREY code
used?
Gray codes are widely
used to prevent spurious output from electromechanical switches and to
facilitate error correction in digital communications such as digital
terrestrial television and some cable TV systems.
1.5 Convert one type of code to another.
1.6 Describe the method of error
detection and correction by using Parity bit.
1.7 Describe the function of Hamming
code.
CODES
BCD,
XS-3, Gray Code, Alphanumeric Codes (ASCII, EBCDIC), Error detecting and
correcting codes (Parity Code, Hamming Code)
Classification of codes
Codes
Weighted Codes
Non-weighted Code
Reflective Codes
Sequential Code
Alphanumeric Error
detecting and correcting Codes
1.
Weighted Codes
•Obey
positional weight principle.
•A
specific weight is assigned to each position of the number. Eg. : Binary, BCD codes
2.
Non-weighted Codes
•Do not
obey the positional weight principle.
•Positional
weights are not assigned.
•Eg.: excess-3 code, Gray code
3.
Reflective Codes
•A code
is said to be reflective when code for 9 is the complement of code for 0, code for
8 is the complement of code for 1, code for 7 is the complement of code for 2, code for
6 is the complement of code for 3, code for 5 is the complement of code for 4.
•Reflectivity
is desirable when 9’s complement has to be found.
•Eg.: excess-3 code
4.
Sequential Codes
•A code
is said to be sequential when each succeeding code is one binary number greater
than preceding code.
•Eg.:
Binary, XS-3
5.
Alphanumeric Codes
•Designed
to represent numbers as well as alphabetic characters.
•Capable
of representing symbols as well as for instructions.
•Eg.:
ASCII, EBCDIC
6.
Error Detecting and Correcting Codes
•When
digital data is transmitted from one system to another, an unwanted electrical
disturbance called ‘noise’ may get added to it.
•This
can cause an ‘error’ in digital information. That means a 0 can change to 1 or
1 can change to 0.
•To
detect and correct such errors special types of codes capable of detecting and
correcting the errors are used.
•Eg.: Parity code, hamming
code.
BCD (Binary Coded Decimal)
Code
•In this
code each digit is represented by a 4-bit binary number.
•The positional weights
assigned to the binary digits in BCD code are 8-4-2-1 with 1 corresponding to
LSB and 8 correspond to MSB.
•Other BCD codes like 7-4-2-1,
5-4-2-1 etc. also exist.
Conversion from decimal to
BCD
•The decimal digits 0 to 9 are
converted into BCD, exactly in the same way as binary.
Invalid BCD codes:
•With 4
bits we can represent a total of sixteen numbers (0000 to 1111) but in BCD only
first, ten codes are used (0000 to 1001)
•Therefore remaining six codes
(1010 to 1111) are invalid in BCD
Conversion of bigger decimal
numbers to BCD:
•Express
each decimal digit with its equivalent 4-bit BCD code
•Eg.: Convert (964)10to its equivalent BCD code.
There fore (964)10=
(1001 0110 0100)BCD
•Hence smallest number in BCD
is 0000 i.e., 0 and largest is 1001 i.e., 9 after which 10 will be expressed by
combinations i.e., 0001 0000, and is known as packed BCD
Comparison with Binary:
•Less efficient than binary,
since the conversion of a decimal number into BCD needs more bits than in binary
Eg., (22)10= (10110)2= (0010 0010)BCDSo BCD uses more bits than
binary for the same decimal number.
•BCD
arithmetic is more complicated than binary arithmetic.
•BCD –decimal conversion is
simpler than Binary –decimal conversion.
|
Decimal Number → |
9 |
6 |
4 |
|
Binary Equivalent → |
1001 |
0110 |
0100 |
Advantages of BCD codes:
•Its
similar to the decimal number system.
•We need
to remember binary equivalents of decimal numbers 0 to 9 only.
•Conversions from decimal to
BCD or BCD to decimal is very simple and no calculation is needed.
Disadvantages of BCD codes:
•Less
efficient than binary, since the conversion of a decimal number into BCD needs more
bits than in binary
•BCD arithmetic is more
complicated than binary arithmetic.
-------------------------------------------------------------------------------------------------------------
Convert the following decimal
numbers to BCD:
(a)164 (b) 4297 (c) 8065
Convert following BCD codes
to decimal equivalent:
(a)1001 1000 (b) 0001 0100 0110 (c) 0111 0011 0101
Convert the following binary
numbers to BCD codes :(
Hint: convert to decimal first)
(a) 1100 (b) 10001 (c) 1010101
Convert following BCD codes
to binary equivalent :(
Hint: convert to decimal first)
(a) 0010 1000(b) 1001 0111(c) 1000 0000
XS-3 (Excess-3)Code
•Non-weighted
code.
•Derived from BCD code
(8-4-2-1 code)words by adding (0011)2 or (3)10 to each codeword.
Decimal BCD XS-3
•Therefore Hence smallest
number in XS-3 is 0011 i.e., 0, and largest is 1100 i.e., 9
Write each digit in 4-bit binary code
|
+ (0011)Decimal |
BCD |
XS-3 |
|
0 |
0000 |
0011 |
|
1 |
0001 |
0100 |
|
2 |
0010 |
0101 |
|
3 |
0011 |
0110 |
|
4 |
0100 |
0111 |
|
5 |
0101 |
1000 |
|
6 |
0110 |
1001 |
|
7 |
0111 |
1010 |
|
8 |
1000 |
1011 |
|
9 |
1001 |
1100 |
Conversion of decimal numbers
XS-3 code:
•Eg.: Convert (964)10to its equivalent XS-3 code.
Therefore (964)10=
(1100 1001 0111)XS-3
Conversion of XS-3 code to
equivalent decimal numbers :
•Eg.: Convert (0011 1010 1100)XS-3to its equivalent decimal
number.
Therefore (1010 0011 1100)XS-3=
(709)10
Obtain XS-3 equivalent of
following numbers:
(a) (235)10(b) (146)10(c) (0111 1000)BCD(d) (1001 0011)BCD
|
(e) (101010)2(hint: first convert to
decimal)Decimal
Number → |
9 |
6 |
4 |
|
XS-3 Equivalent → |
1100 |
1001 |
0111 |
Gray Code
•Non-weighted
code.
•It has a very special feature
that only one bit will change, each time the decimal number is incremented,
therefore also called unit distance code.
Binary and Gray conversions:
•For Gray to binary or binary to
Gray conversions let’s understand rules for Ex-OR
(Ex-OR is represented by symbol)
|
Rules for EX-OR: Decimal |
Binary |
Gray Code |
|
0 |
0000 |
0000 |
|
1 |
0001 |
0001 |
|
2 |
0010 |
0011 |
|
3 |
0011 |
0010 |
|
4 |
0100 |
0110 |
|
5 |
0101 |
0111 |
|
6 |
0110 |
0101 |
|
7 |
0111 |
0100 |
|
8 |
1000 |
1100 |
|
9 |
1001 |
1101 |
|
10 |
1010 |
1111 |
|
11 |
1011 |
1110 |
|
12 |
1100 |
1010 |
|
13 |
1101 |
1011 |
|
14 |
1110 |
1001 |
|
15 |
1111 |
1000 |
Conversion from Binary to
Gray code:
Step 1: Write MSB of given
Binary number as it is.
Step 2: Ex-OR this bit with the next bit of that binary number and write the result.
Step 3: Ex-OR each successive
sum until the LSB of that binary number is reached.
•Eg.: Convert (1010011)2to its equivalent Gray code.
1010011
1111010
Therefore (1010011)2= (1111010) Gray
Conversion from Gray to
Binary:
Step 1: Write MSB of given
Binary number as it is.
Step 2: Ex-OR this bit with the next bit of that binary number and write the result.
Step 3: Continue this process
until the LSB of that binary number is reached.
•Eg.: Convert (1010111)Gray to its equivalent Binary
number.
1010111
1100101
Therefore (1010111)Gray = (1100101)2
Alphanumeric Codes
•A binary
bit can represent only two symbols ‘0’ and ‘1’. But it is not enough for
communication between two computers because there we need many more symbols for
communication.
•These
symbols are required to represent
-26
alphabets with capital and small letters
-Numbers
from 0 to 9
-Punctuation
marks and other symbols
•Alphanumeric
codes represent numbers and alphabetic characters. They also represent other
characters such as punctuation symbols and instructions for conveying
information.
•Therefore instead of using only single binary bits, a
group of bits is used as a code to represent a symbol.
The
ASCII code
Encode the following in ASCII
code:
1. We the people
ASCII-(American Standard Code
for Information Interchange)
•Universally
accepted alphanumeric code.
•Used in
most computers and other electronic equipment. Most computer keyboards are
standardized with ASCII.
•When a key is pressed, its corresponding ASCII code is generated which goes to the
computer.
•Contains
128 characters and symbols.
•Since
128 = 27hence we need 7 bits to write 128 characters. Therefore ASCII is a 7
bit code.
•Can be
represented in 8 bits by considering MSB = 0 always.
•Hence we
have ASCII codes from 0000 0000 to 0111 1111 in binary or from 00 to 7F in
hexadecimal.
•The
first 32 characters are non-graphic control commands (never displayed or
printed) eg. null, escape
•The
remaining characters are graphic symbols (can be displayed and printed). This
includes alphabets (capital and small), punctuation signs, and commonly used
symbols.
•So ASCII code consists of 94 printable characters, 32
non-printable control commands and “Space” and “Delete” characters = 128
characters
----------------------------------------------------------------------------------------------------------------------------
Using ASCII table obtain
ASCII code word for
(a) DEL, (b) %, ( c) W, (d)
g, (e) &
EBCDIC-(Extended Binary
Coded Decimal Interchange Code)
•8-bit
code.
•Total
256 characters are possible, however, all are not used.
•There is no parity bit used to check error in this
code set.
--------------------------------------------------------------------------------------------------------------------
Using code table obtain
EBCDIC code word for
(a)
NUL, (b) & (c) m (d) SP (e) –
Error detecting and
correcting codes
•When a
digital information is transmitted, it may not be received correctly by the
receiver.
•The
error is caused due to electrical disturbance of circuit it is also called
noise.
•This
noise may force ‘1’ to change to ‘0’ or vice versa.
•This error has to be detected and corrected.
---------------------------------------------------------------------------------------------------------------
Parity:
•For
detection of error an extra bit (parity bit) is attached to code.
•For
example: If a 7-bit data (1010110) is to be transmitted then it can be
transmitted as 8-bit word (01010110) i.e., even parity codeword or as
(11010110) i.e., odd parity codeword.
•Where
parity is decided by extra MSB (parity bit) which is introduced in original
data.
•If total
number of ‘1’s in transmitted/ received word is even then parity is even.
•If total number of ‘1’s in transmitted/ received word
is odd then parity is odd.
1.7 Describe the function of Hamming
code.
Hamming Code - Error Detection and Error
Correction AUGUST 10, 2021
The hamming code technique, which is an error-detection and
error-correction technique, was proposed by R.W. Hamming. Whenever a
data packet is transmitted over a network, there are possibilities that the
data bits may get lost or damaged during transmission.
Let's understand the Hamming code concept with an example:
Let's say you have received a 7-bit Hamming code which is
1011011.
First, let us talk about the redundant bits.
The redundant bits are some extra binary bits that are
not part of the original data, but they are generated & added to the
original data bit. All this is done to ensure that the data bits don't get
damaged and if they do, we can recover them.
Now the question arises, how do we determine the number of
redundant bits to be added?
We use the formula, 2r >= m+r+1; where r = redundant bit & m = data bit.
From the formula we can make out that there are 4 data bits
and 3 redundancy bits, referring to the received 7-bit hamming code.
What is Parity Bit?
To proceed further we need to know about parity bit,
which is a bit appended to the data bits which ensures that the total number of
1's are even (even parity) or odd (odd parity).
While checking the parity, if the total number of 1's are odd
then write the value of parity bit P1(or P2 etc.) as 1
(which means the error is there ) and if it is even then the value of the parity the bit is 0 (which means no error).
Hamming Code: Error Detection
As we go through the example, the first step is to identify the
bit position of the data & all the bit positions which are powers of 2 are
marked as parity bits (e.g. 1, 2, 4, 8, etc.). The following image will help in
visualizing the received hamming code of 7 bits.
First, we need to detect whether there are any errors in this
received hamming code.
Step 1: For checking parity bit P1,
use check one and skip one method, which means, starting from P1 and
then skip P2, take D3 then skip P4 then take D5, and then skip D6 and take D7,
this way we will have the following bits,
As we can observe the total number of bits is odd so we will
write the value of parity bit as P1 = 1. This means the error is there.
Step 2: Check for P2 but while
checking for P2, we will use the check two and skip two methods, which will
give us the following data bits. But remember since we are checking for P2, so
we have to start our count from P2 (P1 should not be considered).
As we can observe that the number of 1's are even, then we will
write the value of P2 = 0. This means there is no error.
Step 3: Check for P4 but while
checking for P4, we will use the check four and skip four methods, which will
give us the following data bits. But remember since we are checking for P4, so
we have started our count from P4(P1 & P2 should not be considered).
As we can observe that the number of 1's are odd, then we will
write the value of P4 = 1. This means the error is there.
So, from the above parity analysis, P1 & P4 are not equal to
0, so we can clearly say that the received hamming code has errors.
Hamming Code: Error Correction
Since we found that the received code has an error, so now we must
correct them. To correct the errors, use the following steps:
Now the error word E will be:
Now we have to determine the decimal value of this error word 101
which is 5 (22 *1 + 21 * 0 + 20 *1 = 5).
We get E = 5, which states that the error is in the fifth
data bit. To correct it, just invert the fifth data bit.
So the correct data will be:
Conclusion:
So in this article, we have seen how the hamming code technique
works for error detection and correction in a data packet transmitted over a
network.
1.8 Describe the applications of codes.
What's the use of
coding?
Simply put, coding is used for communicating with computers.
People use coding to give computers and other machines instructions on what
actions to perform. Further, we use it to program the websites, apps, and other
technologies we interact with every day.
What is APPlication
source code?
Source code is the
list of human-readable instructions that a programmer writes—often in a
word processing program—when he is developing a program. The source code is run
through a compiler to turn it into machine code, also called object code, that
a computer can understand and execute.
Where is coding used
in everyday life?
Programming is everywhere
in the modern world and meets you in the street, your workplace, and the
local grocery store. You interact with bar-code scanners regularly, and you
almost certainly use lots of code while working, whether you're using a word
processor to write a letter or an email platform to send messages.
How do you explain a
program?
In computing, a program
is a specific set of ordered operations for a computer to perform. In
the modern computer that John von Neumann outlined in 1945, the program
contains a one-at-a-time sequence of instructions that the computer follows.
Typically, the program is put into a storage area accessible to the computer.
What is difference
between source code and object code?
The basic difference
between source code and object code is that source code is written by a
programmer while an object code is produced when a source code is compiled.
Source code is created with a text editor or a visual programming tool and then
saved in a file and object code is processed by the CPU in a computer.
Why source code is
important?
Source code serves the
needs of companies who have procedures in place that they want to retain
regardless of the software installed. Some companies consider source code as a
way to guarantee that the software changes as their company's needs change in
the future.
What are the
advantages of coding?
Why learn to code? 6 Surprising benefits to consider
·
Coding and programming
careers have great earning potential. ...
·
Demand remains strong
for coding-related jobs. ...
·
Coding ability gives a new perspective to problem-solving. ...
·
Learning to code
offers career flexibility. ...
·
Learning to code can
be a fun bonding opportunity for families.
What are the 4 types
of programming language?
The 4 types of programming Language that is classified are:
·
Procedural Programming
Language.
·
Functional Programming
Language.
·
Scripting Programming
Language.
·
Logic Programming
Language.
·
Object-Oriented
Programming Language.
Apr 21, 2021
What are the seven
major steps in programming?
The seven steps of
programming.
·
Step 1: Define the
Program Objectives. ...
·
Step 2: Design the
Program. ...
·
Step 3: Write the
Code. ...
·
Step 4: Compile. ...
·
Step 5: Run the
Program. ...
·
Step 6: Test and Debug
the Program. ...
·
Step 7: Maintain and
Modify the Program.
Which is the No 1
programming language?
PYPL Index: The PYPL
PopularitY of Programming Language Index is created by analyzing how often
language tutorials are searched on Google. The index is updated once a month.
...
PYPL Index (US)
|
Aug 2021 |
Programming language |
Share |
|
1 |
Python |
31.47 % |
|
2 |
Java |
19.14 % |
|
3 |
JavaScript |
7.49 % |
|
4 |
C# |
6.24 % |
What are the main
steps to develop a program?
The following are six
steps in the Program Development Life Cycle:
·
Analyze the problem.
The computer user must figure out the problem, then decide how to resolve the
problem - choose a program.
·
Design the program.
...
·
Code the program. ...
·
Debug the program. ...
·
Formalize the
solution. ...
·
Document and maintain
the program.
What are the five
steps in program planning?
·
Determine your
personal needs.
·
Consider your program
options.
·
Set goals.
·
Structure your program
and write it down.
·
Keep a log and
evaluate your program.
2. Understand
the basic digital circuits.
2.1 Describe the digital
signals.
2.2 State the main
features of digital systems.
2.3 Describe AND, OR,
NOT, NAND, NOR, and XOR operations.
2.4 Describe the
realization of basic logic operations using NAND and NOR gates.
2.5 Describe the
Boolean algebraic theorems.
2.6 Simplify the logic
expressions by using Boolean algebra.
2.7 Simplify the logic
expressions by using the Karnaugh map (up to 4 Variables).
2.8 Describe the
characteristics of digital ICs.
2.9 Describe different types of digital logic
families.
3. Understand
Combinational Logic Circuits.
3.1 Describe the
operation of a digital multiplexer and DE multiplexer.
3.2 Describe the
operation of half adder and full adder.
3.3 Describe the
operation of half subtractor and full subtractor.
3.4 Explain the function
of arithmetic logic unit (ALU) with block diagram.
3.5 Describe the
operation of digital comparators.
1.7 Describe the function of parity generator/checkers.
1.8 Describe the function of priority encoders and
BCD-to-7 segment decoder with block diagram
4. Understand
Flip-Flops and shift registers.
4.1 Describe the
operation of a sequential circuit with a block diagram.
4.2 Describe the
working principle of clocked SR flip-flop, D-type flip-flop, and T-type
flip-flop J-K flip-flop, Master-slave flip-flop.
4.3 State the
applications of flip-flops.
4.4 Describe the
function of registers.
4.5 Describe the
operation of shift registers.
4.6 Mention the
applications of shift registers.
4.7 List some common ICs used as flip-flops and
shift registers.
5. Understand
the Counters.
5.1 Describe the operation of ripple or asynchronous counters.
5.2 Describe the principle of UP/DOWN counters.
5.3 Describe the modulus of the Counter.
5.4 Describe the operation of synchronous counters.
5.5 Explain the function of the universal counter.
5.6 Describe the principle of the ring counter.
5.7 List some
common ICs used as a counter with a block diagram.
6. Understand the D/A converter.
6.1 Mention the principle of level conversion.
6.2 Describe the principle of D/A conversion.
6.3 Mention the types of D/A converter.
6.4 Explain the operation of a binary-weighted D/A and R-2R
ladder D/A converter.
6.5 State the terms – resolution, percentage of resolution,
accuracy.
6.6 Offset error and settling time as the specification of the D/A
converter.
6.7 State the application field of the D/A converter.
6.8 List the application of popular D/A converter ICS.
7. Understand
A/D converter.
7.1 State the principle of A/D conversion.
7.2 List the type of A/D converter.
7.3 State the working principle of a 3-bit parallel A/D converter.
7.4 Describe the operation of the Digital Ramp A/D converter
7.5 Explain the principle of operation of successive
approximation, dual-slope, and Flash A/D converter.
7.6 State the terms – resolution, accuracy, and conversion time
as the specification of the A/D converter.
7.7 List the applications of popular A/D converter ICS.
7.8 Describe the
operation of sample & hold circuits and their application.
8. Understand
the features of Semiconductor Memories.
8.1 Describe the operation of a memory device with a block
diagram.
8.2 Describe the concept of READ and WRITE operation of
memories.
8.3 Mention the classification of memories.
8.4 Mention the characteristics of memories.
8.5 Explain the principle of sequential memory.
8.6 Mention the characteristics of ROM, PROM, EPROM, EEPROM and
Flash memory.
8.7 Mention the principle of static and dynamic RAM.
8.8 List some
commercial memory ICs.
9. Understand
the features of the Microprocessor.
9.1 Define Microprocessor.
9.2 List 8-bit, 16-bit, 32 bit and 64-bit Microprocessors.
9.3 Describe the architecture of the 8085 microprocessor.
9.4 Describe the pin diagram and function of each pin of Intel
8085 microprocessors.
9.5 Describe the registers of Intel 8085 microprocessors.
9.6 Describe the block diagram of a microcomputer.
9.7 Differentiate
between microprocessors and microcomputers.
10. Understand
the Programming of 8085 Microprocessors.
10.1 Describe the instruction set of 8085 microprocessors.
10.2 Explain the addressing modes of Intel 8085 microprocessors.
10.3 Mention the
simple programs using 8085 instructions.
11. Understand
the 8085 Microprocessors system.
11.1 Define Bus multiplexing.
11.2 Explain the process of multiplexing the AD7 -AD0 bus using a latch.
11.3 Describe the technique of generating control signals.
11.4 Mention the function of interrupt controls and serial I/O
controls.
11.5 Differentiate between memories mapped I/O and standard I/O.
11.6 Discuss the function of programmable peripheral Interface
(PPI), programmable DMA controller and programmable interrupt controller (PIC).
11.7 Discuss the function of the Programmable Interval Timer and
Programmable Communication Interface.
11.8 Draw an 8085
based microcomputer system.
12. Understand
the features of 16-bit Microprocessors.
12.1 Describe the architecture of the 8086 microprocessor.
12.2 Describe the pin diagram and function of each pin of Intel
8086 microprocessors.
12.3 Describe the registers of Intel 8086 microprocessors.
12.4 Explain the addressing modes of the Intel 8086
microprocessors.
12.5 Mention the
simple programs using the 8086 instructions.
PRACTICAL:
1. Verify the
truth tables of logic gates (OR, AND, NOT, NAND & NOR)
1.1 Select logic gate ICs.
1.2 Select appropriate circuits, required tools, equipment’s and
materials.
1.3 Insert the selected IC into the Breadboard.
1.4 Connect the circuits as per the diagram on the trainer board.
1.5 Switch on the DC power supply,
1.6 Verify the
truth tables.
2. Show the
operation of NAND & NOR gate as universal gates.
2.1 Select logic gate IC of NAND gate & NOR gate.
2.2 Select appropriate circuits, required tools, equipment’s and
materials.
2.3 Insert the selected IC into the Breadboard.
2.4 Connect the circuits as per diagram for AND OR & NOT
gate on trainer board.
2.5 Switch on the DC power supply,
2.6 Verify the
truth tables of AND OR & NOT gate operation.
3. Verify the
functions of half adder & half subtractor.
3.1 Select ICs.
3.2 Draw the pin diagram and internal connection.
3.3 Draw appropriate circuits.
3.4 Select required tools, equipment’s and materials.
3.5 Connect the circuits as per the diagram on the trainer board.
3.6 Switch on the DC power supply,
3.7 Verify the
truth tables.
4. Verify the
functions of full adder & full subtractor.
4.1 Select ICs.
4.2 Draw the pin diagram and internal connection.
4.3 Draw appropriate circuits.
4.4 Select required tools, equipment’s and materials.
4.5 Connect the circuits as per the diagram on the trainer board.
4.6 Switch on the DC power supply.
4.7 Verify the
truth tables.
5. Verify the truth table of different J-K flip-flops.
5.1 Select appropriate ICs.
5.2 Draw the pin diagram and internal connection.
5.3 Draw appropriate circuits.
5.4 Select required tools, equipment’s and materials.
5.5 Connect the circuits as per the diagram on the trainer board.
5.6 Switch on the DC power supply.
5.7 Verify the
truth tables.
6. Verify the
operation of the Shift register.
6.1 Select a SIPO shift register IC.
6.2 Connect the SIPO shift register circuits on Digital Trainer
Board.
6.3 Apply clock input pulse to the circuit and observe the
operation.
6.4 Select a PISO shift register IC.
6.5 Connect the PISO shift register circuits on Digital Trainer
Board.
6.6 Apply clock
input pulse to the circuit and observe the operation.
7. Verify the
operation of the Binary counter.
7.1 Select 4-Bit ripple counter IC.
7.2 Connect the Up/Down ripple counter circuit on Digital
Trainer Board
7.3 Apply clock input pulse to the circuit and observe the
operation of up-counting and down counting.
7.4 Select MOD-10 counter IC.
7.5 Connect the Decade counter circuit on Digital Trainer Board.
7.6 Apply clock
input pulse to the circuit and observe the Decade operation.
8. Verify the
operation of D/A converter.
8.1 Select a D/A converter IC.
8.2 Connect a ladder R/2R D/A converter circuit on Digital
Trainer Board.
8.3 Apply input data and clock pulses to the different inputs of
the circuit.
8.4 Observe the operation
of the circuit and detect the output result of the D/A converter
9. Verify the
operation of the A/D converter.
9.1 Select an A/D
converter IC.
9.2 Connect a 3-bit
parallel A/D converter circuit on Digital Trainer Board.
9.3 Apply input data
and clock pulses to the different inputs of the circuit.
9.4 Observe the operation of the circuit and detect
the output result of the A/D converter.
10. Verify the
operation of SRAM & DRAM.
10.1 Select an SRAM IC.
10.2 Connect Static
RAM circuit on Digital Trainer Board.
10.3 Apply input data
and clock pulse to the circuit.
10.4 Observe the
operation of the circuit and stored memory data in the SRAM.
10.5 Select a DRAM IC.
10.6 Connect Dynamic
RAM circuit on Digital Trainer Board.
10.7 Apply input data
and clock pulse to the circuit.
10.8 Observe the operation of the circuit and
stored memory data in the DRAM.
11. Verify the
operation of an EPROM.
11.1 Select an EPROM IC.
11.2 Connect EPROM circuit on Digital Trainer Board.
11.3 Apply input data and clock pulse to the circuit.
11.4 Observe the
operation of the circuit and stored memory data into the EPROM.
12. Verify the
operation of 8085 Microprocessor.
12.1 Select 8085 microprocessor trainer
board.
12.2 Solve simple arithmetic &
logical problems.
12.3 Monitor the result into the Matrix
display/LCD display.
12.4 Solve simple I/O problems.
