EDAC TECHNIQUES TRAINER BOARD

CONTENTS

S NO. DESCRIPTION PAGE

1. Introduction to Error Detection & Correction Techniques 2

2. Block Diagram of EDAC Trainer Kit 6

3. Pictorial View of EDAC Trainer 7

4. Experiment Selection Table 8

5. Exp 1(a):- To Detect the error in 8-bit binary data using Even Parity. 9

6. Exp 1(b):- To Detect the error in 8-bit binary data using Odd Parity. 12

7. Exp 2:- To Generate Checksum & detect error in Received Data 15

8. Exp 3:- To Detect an error using Cyclic Redundancy Check Method 18

(CRC)

9. Exp 4(a):- To calculate Hamming Parity bits in 8-bit Binary data & 21

generate that Frame.

10. Exp 4(b):- To Generate Error in Transmitted Hamming Data Frame. 30

11. Exp 4(c):- To Correct Error in Transmitted Hamming Data Frame. 32

12. Exp 4(c):- To Transmit 8-bit binary Data using Hamming Encoding & 34

Decoding Technique without error.

13. Exp 4(c):- To Transmit 8-bit binary Data using Hamming Encoding & 36

Decoding Technique with an error.

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Introduction

ERROR DETECTION AND CORRECTION

Error detection and correction (EDAC) techniques are used to ensure that data is correct and has
not been corrupted, either by hardware failures or by noise occurring during transmission or a
data read operation from Memory. There are many different error correction codes in existence.
The reason for the different codes being used in different applications has to do with the
historical development of the data storage, the types of data errors occurring, and the overhead
associated with each of the error detection techniques. We discuss some of the popular
techniques here with details of hamming code.

PARITY CODE:-
When a word is written into memory, each parity bit is generated from the data bits of the byte it
is associated with. This is done by a tree of Exclusive-OR gates. When the word is read back
from the memory, the same parity computation is done on the data bits read from the memory,
and the result is compared to the parity bits that were read. Any computed parity bit that doesn't
match the stored parity bit indicates that there was at least one error in that byte (or in the parity
bit itself). However, parity can only detect an odd number of errors. If an even number of errors
occurs, the computed parity will match the read parity, so the error will go undetected. Since
memory errors are rare if the system is operating correctly, the vast majority of errors will be
single-bit errors, and will be detected. Unfortunately, while parity allows for the detection of
single bit errors, it does not provide a means of determining which bit is in error, which would be
necessary to correct the error. Thus the data needs to be read again if an error is detected. Error
Correction Code (ECC) is an extension of the parity concept.

CHECKSUM CODE:-
This is a kind of error detection code used for checking a large block of data. The checksum bits
are generated by summing all the codes of a message and are stored with data. Usually the block
of data summed is of length 512 or 1024 and the checksum results are stored in 32 bits that
allows overflow. When data is read the summing operation is again done and checksum bits
generated are matched with the stored one. If they are unequal then an error is detected.
Obviously, it can fool the detection system if error occurring at one place is compensated by the
other.

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CYCLE REDUNDANCY CODE (CRC):-

This is a more robust error checking algorithm than the previous two. The code is generated like
this. Take a binary message and convert it to a polynomial then divide it by another predefined
polynomial called the key. The remainder from this division is the CRC. This is stored with the
message. Upon reading the data, memory controller does the same operation i.e. divides the
message by the same key and compares with CRC stored. If they differ, the data is wrongly read
or stored. Not all keys are equally good. The longer the key, the better is the error checking. On
the other hand, the calculations with long keys can get pretty involved. Two of the polynomials
commonly used are:
CRC-16 = x16 + x15 + x2+ 1
CRC-32 = x32 + x26 + x23 + x22 + x16 + x12 + x11 + x10 + x8 + x7 + x5 + x4 + x2 + x + 1
Usually, series of Ex-OR gates are used to generate CRC code.

HAMMING CODE:-
Introduced in 1950 by R.W. Hamming, this scheme allows one bit in the word to be corrected,
but is unable to correct events where more than one bit in the word is in error. These multi-bit
errors can only be detected, not corrected, and therefore will cause a system to malfunction.
Hamming code uses parity bits discussed before but in a different way. For n number of data
bits, number of parity bits required here if m then
2m _ m + n + 1

In the memory word, (i) all bit positions that are of the form 2i are used as parity bits
(like 1,2,4,8,16,32…..) and (ii)the remaining positions are used as data bits
(like3,5,6,7,9,10,11,12,13,14,17,18…….) Thus code will be in the form of P3 P2 D7 P1 D6 D5
D4 P0 D3 D2 D1 D0………. Where P3 P2,P1,P0…. are parity bits and D7, D6, D5, D4,
D3,D2,D1,D0….are data bits We discuss Hamming Code generation with an example. Consider
the 8-bit data to be coded is 11000100. This requires 4 parity bits in position 1,2,4,8 so that
Hamming coded data becomes 12 bit long. To calculate the value of P3 we check parity of zeroth
binary locations of data bits. This is shown in 3rd row of Fig.1 for this example. Zeroth locations
are the places where address ends with an 1. These are D7, D6, D4, D3, D1 for 8 bit data. Since
we have total even number of 1s in these 3 positions P3=0. This is calculated as done in case of
parity generation by series of Ex-OR gates through equation
P3 = D7 D6 D4 D3 D1

Similarly for P2, we check locations where we have 1 in address of the 1st bit i.e. D7,
D5, D4, D2,D1. Since there are even number of 1s, P2=0. Proceeding in similar manner and
examining parity of P1=1 and P0=1.

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P3 P2 D7 P1 D6 D5 D4 P0 D3 D2 D1 D0

Data Word 1 1 0 0 0 1 0 0
(without
parity)
P3 0 1 1 0 0 0

P2 0 1 0 0 1 0

P1 1 1 0 0 0

P0 1 0 1 0 0

Data with 0 0 1 1 1 0 0 1 0 1 0 0
parity
Fig.1 Calculation of parity bits

Next we discuss how error in a hamming coded data is detected and if it is in single bit how it is
corrected. We continue with the previous example and consider the data is incorrectly read in
position D0 so that 12 bit coded data is 001110010100. Fig.2 describes the detection mechanism.
First of all, we check the parity of zeroth position and find it is to be even. Since P1=1, this
parity check fails and this is equivalent to generating a parity bit at the output (last column)
following equation Parity P1 check bit = D6 D5 D4 D0 P1. Note that, in addition to data bits
we have also included the corresponding parity bit to the input of Ex-OR gate tree. Note that,
even a single failure detects an error. However, to correct the error, we use the output of last
column 0011 (in the order P3 P2 P1 P0) and find its decimal equivalent which is 12. So the data
of location 12, which is D0 needs to be corrected.

P3 P2 D7 P1 D6 D5 D4 P0 D3 D2 D1 D0 Parity Parity
check bit
Received 0 0 1 1 1 0 0 1 0 1 0 1
data
word
P3 0 1 1 0 0 0 Pass 0
P2 0 1 0 0 1 0 Pass 0
P1 1 1 0 0 1 Fail 1
P0 1 0 1 0 1 Fail 1
Fig.2 Error detection and correction

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Note that, this method detects error in more than one position unlike the first method but
overhead is more. In simple parity method we add 1 additional bit for 12 bit data while this is 4
here. Also note, further increasing this overhead, error in more than one position can also be
corrected. However, more than one bit error is unlikely for memory read. With overhead for 1 bit
correction, if error occurs in more than 1 bit positions the data needs to be read once again from
the memory.

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BLOCK DIAGRAM OF EDAC TRAINER

Block Diagram of EDAC Kit

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Pictorial View of Hamming Code Trainer

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EXPERIMENTS SELECTION TABLE

SR. SELECTION EXPERIMENT EXPERIMENT
NO SWITCH SELECTED NO.
1. 0001 EVEN PARITY 1(A)
2. 0010 ODD PARITY 1(B)
3. 0011 CHECK SUM 2
4. 0100 CRC CODE 3
5. 1000 HAMMING CODE 4

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Experiment No: - 1(A)

Aim:-To detect the error in 8 bit binary data using even parity.

Equipment required:-EDAC Techniques Trainer Kit, CRO/DSO, Connecting probes,

Power Cord.

Theory:-
A parity bit, or check bit, is a bit added to the end of a string of binary code that indicates
whether the number of bits in the string with the value one is even or odd. Parity bits are used as
the simplest form of error detecting code.
There are two variants of parity bits: even parity bit and odd parity bit. In case of even parity, the
parity bit is set to 1, if the number of ones in a given set of bits (not including the parity bit) is
odd, making the number of ones in the entire set of bits (including the parity bit) even. If the
number of ones in a given set of bits is already even, it is set to a 0. Even parity is a special case
of a cyclic redundancy check (CRC), where the 1-bit CRC is generated by the polynomial x+1.
In mathematics, parity refers to the evenness or oddness of an integer, which for a binary
number is determined only by the least significant bit. In telecommunications and computing,
parity refers to the evenness or oddness of the number of bits with value one within a given set of
bits, and is thus determined by the value of all the bits. It can be calculated via an XOR sum of
the bits, yielding 0 for even parity and 1 for odd parity. This property of being dependent upon
all the bits and changing value if any one bit changes allow for its use in error detection schemes.

Procedure:-
1.Connect the power cord and Switch on the Experiment kit.
2.First insert the selected data using the data switches i.e. D0-D7.

Example:
To transmit the data
1 0 1 1 1 0 0 1
D7 D6 D5 D4 D3 D2 D1 D0

Put the data switches as

OFF

ON

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In this transmitted data there is five 1 bits or we can say no even number of 1’s, so the
parity bit is set to 1.

DATA = 10111001 (From Data Generator Switches)

Even Parity=1 + 0 + 1 +1 + 1 + 0 + 0 + 1 =1 (LED P(0) will indicate the Even Parity)

Data Frame =101110011 (Data Frame Tx LED (T8 to T0) will show the data frame)

3. Now connect the Tx with Rx and GND (Tx) with GND (Rx).
We can check the Tx data and Data clk on the DSO or CRO, and also can change the Data
frequency by the Frequency selector switch.
At the receiving end the R0 to R7 is data and R8 is Parity Bit. Now from the received data
(R7 to R0) the Even parity is again calculated in the decoder and shown on LED C(0). If
the received parity and calculated parity matches then there is no error in the received data
and Green Led will glow and received data is shown on Rx data D’(7) to D’(0).
4. If we insert an error in the data frame at the transmitter end by making the respective error
switches ON. Whenever we generate an error in the tx data frame the parity information
will be changed and error is detected error indicator LED will glow at the receiver and no
data is shown at the received data. The Even Parity method can detect only one BIT of
ERROR.

WAVEFORMS:-

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FIG 1(A).1: SERIAL DATA TX AND DATA CLOCK WITHOUT ERROR

FIG 1(A).2: SERIAL DATA TX AND DATA CLOCK WITH ERROR IN BIT D(4)

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Experiment No: - 1(B)

Aim:-To detect the error in 8 bit binary data using odd parity.

Equipment Required:- EDAC Techniques Trainer Kit, CRO/DSO, Connecting probes,

Power Cord.

Theory:-
A parity bit, or check bit, is a bit added to the end of a string of binary code that indicates
whether the number of bits in the string with the value one is even or odd. Parity bits are used as
the simplest form of error detecting code. There are two variants of parity bits: even parity
bit and odd parity bit. When using odd parity, the parity bit is set to 1 if the number of ones in a
given set of bits (not including the parity bit) is even, making the number of ones in the entire set
of bits (including the parity bit) odd. When the number of set bits is odd, then the odd parity bit
is set to 0. Even parity is a special case of a cyclic redundancy check (CRC), where the 1-bit
CRC is generated by the polynomial x+1.
In mathematics, parity refers to the evenness or oddness of an integer, which for a binary
number is determined only by the least significant bit. In telecommunications and computing,
parity refers to the evenness or oddness of the number of bits with value one within a given set of
bits, and is thus determined by the value of all the bits. It can be calculated via an XOR sum of
the bits, yielding 0 for even parity and 1 for odd parity. This property of being dependent upon
all the bits and changing value if any one bit changes allows for its use in error
detection schemes.
Procedure:-
1.Connect the power cord and Switch on the Experiment kit.
2.First insert the selected data using the data switches i.e. D0-D7.

Example:
To transmit the data
1 0 1 1 1 0 0 1
D7 D6 D5 D4 D3 D2 D1 D0

Put the data switches as

OFF

ON

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In this transmitted data there is five 1 bits or we can say odd number of 1’s, so the parity
bit is set to 0.

DATA = 11011010 (From Data Generator Switches)

Odd Parity=1 + 0 + 1 +1 + 1 + 0 + 0 + 1 =0 (LED P(0) will indicate the Odd Parity)

Data Frame = 101110010 (Data Frame Tx LED (T8 to T0) will show the data frame)

3. Now connect the Tx with Rx and GND (Tx) with GND (Rx).
We can check the Tx data and Data clk on the DSO or CRO, and also can change the Data
frequency by the Frequency selector switch.
At the receiving end the R0 to R7 is data and R8 is Parity Bit. Now from the received data
(R7 to R0) the Odd parity is again calculated in the decoder and shown on LED C(0). If the
received parity and calculated parity matches then there is no error in the received data and
Green Led will glow and received data is shown on Rx data D’(7) to D’(0).
4. If we insert an error in the data frame at the transmitter end by making the respective error
switch ON. Whenever we generate an error in the tx data frame the parity information will
be changed and error is detected error indicator LED will glow at the receiver and no data
is shown at the received data. The Odd Parity method can detect Only one BIT of
ERROR.

WAVEFORM:-

FIG.1(B)1: : SERIAL DATA TX AND DATA CLOCK WITHOUT ERROR

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FIG.1(B)1: : SERIAL DATA TX AND DATA CLOCK WITH ERROR IN BIT D(4)

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Experiment No: - 2
Aim:-To generate checksum and detect error in the received data.

Equipment required: - EDAC Techniques Trainer Kit, CRO/DSO, Connecting probes,

Power Cord.

Theory:-
A checksum or hash sum is a small-size datum computed from an arbitrary block of digital data
for the purpose of detecting errors that may have been introduced during
its transmission or storage. The integrity of the data can be checked at any later time by
recomposing the checksum and comparing it with the stored one. If the checksums match, the
data was likely not accidentally altered. The procedure that yields the checksum from the data is
called a checksum function or checksum algorithm. A good checksum algorithm will yield a
different result with high probability when the data is accidentally corrupted; if the checksums
match, the data has the same high probability of being free of accidental errors.
Checksum functions are related to hash functions, fingerprints, randomization functions,
and cryptographic hash functions. However, each of those concepts has different applications
and therefore different design goals. It is important to not use a checksum in a security related
application, as a checksum does not have the properties required to protect data from intentional
tampering. Check and parity bits are special cases of checksums, appropriate for small blocks of
data (such as numbers, bank numbers, computer words, single bytes, etc.). Some error-correcting
codes are based on special checksums that not only detect common errors but also allow the
original data to be recovered in certain cases.
Procedure:-
1.Connect the power cord and Switch on the Experiment kit.
2.First insert the selected data using the data switches i.e. D0-D7.

Example:
To transmit the data
1 0 1 1 1 0 0 1
D7 D6 D5 D4 D3 D2 D1 D0

Put the data switches as

OFF

ON

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Suppose the following block of 8 bits is to be sent using a checksum of 2 frames of 4 bits, so the
8 bits are grouped in 4-4 bit data with lower 4 bit data switches and upper 4 bit data switches.
1011 1001

The numbers are added

1011
1001
-------------
Sum 1)0100
Checksum 1011 ; complemented
This calculated Checksum is shown on the parity bits P(3) to P(0).
The complete Tx data Frame will be = 1011 1011 1001
This Tx data frame will be shown on the T(11) to T(0)
We can check the Tx data Frame using CRO/DSO at tx test point.
3. Now Connect the Tx with Rx and GND(Tx) with GND(Rx) using Banana connector cable.
4. Now suppose the receiver receives the pattern sent by the Tx is shown on LEDs R(11) to
R(0).
1011 1011 1001
When the receiver calculates the sum of the three sections {R(11) to R(8), R(7) to R(4)
and R(3) to R(0)}, it will get all 1s, which, after complementing, is all 0s and shows that
there is no error.
1011
1011
1001
--------
Sum 1111
Complement 0000
Means that the pattern is OK.

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WAVEFORMS:-

FIG2.1: : SERIAL DATA TX AND DATA CLOCK WITHOUT ERROR

FIG2.1: : SERIAL DATA TX AND DATA CLOCK WITH ERROR IN D(4)

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Experiment No:- 3
Aim:-To detect an error using cyclic redundancy check method.

Equipment Required:- EDAC Techniques Trainer Kit, CRO/DSO, Connecting probes,

Power Cord.

Theory:-
A cyclic redundancy check (CRC) is an error-detecting code commonly used in
digital networks and storage devices to detect accidental changes to raw data. Blocks of data
entering these systems get a short check value attached, based on the remainder of a polynomial
division of their contents; on retrieval the calculation is repeated, and corrective action can be
taken against presumed data corruption if the check values do not match.
CRCs are so called because the check (data verification) value is a redundancy (it expands the
message without adding information) and the algorithm is based on cyclic codes. CRCs are
popular because they are simple to implement in binary hardware, easy to analyze
mathematically, and particularly good at detecting common errors caused by noise in
transmission channels. Because the check value has a fixed length, the function that generates it
is occasionally used as a hash function.
Procedure:-
1.Connect the power cord and Switch on the Experiment kit.

Example:

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The divisor and the data word is generated through the data switches. The divisor is generated
with the help of D0-D3 switches and the data word with the help of D4-D7.
We can check the Tx data Frame using CRO/DSO at tx test point.
2.Now Connect the Tx with Rx and GND(Tx) with GND(Rx) using Banana connector cable.

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WAVEFORMS:-

FIG2.1: : SERIAL DATA TX AND DATA CLOCK WITHOUT ERROR

FIG2.1: - SERIAL DATA TX AND DATA CLOCK WITH ERROR IN D(2)

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Experiment No:-4(A)

Aim:- To Calculate Hamming parity bits in 8 bit binary data and generate data frame.

Equipment Required :- EDAC Techniques Trainer Kit, CRO/DSO, Power Cord.

Theory:-
Hamming Codes are used in detecting and correcting a code. An error-correcting code is an
algorithm for expressing a sequence of numbers such that any errors which are introduced can be
detected and corrected (within certain limitations) based on the remaining numbers. Errors can
happen in a variety of ways. Bits can be added, deleted, or flipped. Errors can happen in fixed or
variable codes. Error-correcting codes are used in CD players, high speed modems, and cellular
phones. Error detection is much simpler than error correction. For example, one or more "check"
digits are commonly embedded in credit card numbers in order to detect mistakes.
In this kit there are 8 data inputs i.e. D0-D7 and four parity bits i.e P0-P3 respectively.
To calculate the parity bits we use the formula which is given below:
P3= D7+D6+D4+D3+D1
P2= D7+D5+D4+D2+D1
P1= D6+D5+D4+D0
P0= D3+D2+D1+D0

Procedure:-
1.Connect the power cord and Switch on the Experiment kit.
2.First insert the selected data using the data switches i.e. D0-D7.
3.We calculate the hamming or we can say parity bits using the below mentioned table:

Binary data Parity bits Complete data frame

D7 D6 D5 D4 D3 D2 D1 D0 P3 P2 P1 P0 T11 T10 T9 T8 T7 T6 T5 T4 T3 T2 T1 T0
P3 P2 D7 P1 D6 D5 D4 P0 D3 D2 D1 D0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 1
0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 0 1 1
0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 1 1
0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 0
0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 1 0 0 0 0 0 1 0 1
0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0
0 0 0 0 0 1 1 1 1 0 1 1 1 0 0 1 0 0 0 1 0 1 1 1
0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0

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0 0 0 0 1 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1
0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0
0 0 0 0 1 0 1 1 0 1 1 1 0 1 0 1 0 0 0 1 1 0 1 1
0 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0
0 0 0 0 1 1 0 1 1 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1
0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1
0 0 0 1 0 0 0 0 1 1 1 0 1 1 0 1 0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 1 1 1 0 1 1 1 0 0 0 0 1 1 0 0 0 1
0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0
0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1
0 0 0 1 0 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 1 0 0
0 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1
0 0 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 0 1 0 0 1 1 0
0 0 0 1 0 1 1 1 0 1 0 1 0 1 0 0 0 0 1 1 0 1 1 1
0 0 0 1 1 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1 0 0 0
0 0 0 1 1 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 1
0 0 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 1 0
0 0 0 1 1 0 1 1 1 0 0 1 1 0 0 0 0 0 1 1 1 0 1 1
0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0
0 0 0 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 1
0 0 0 1 1 1 1 0 1 1 1 1 1 1 0 1 0 0 1 1 1 1 1 0
0 0 0 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0 1 0 1 1 1 1
0 0 1 0 0 0 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 0 0 1
0 0 1 0 0 0 1 0 1 0 1 1 1 0 0 1 0 1 0 1 0 0 1 0
0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1
0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0
0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1
0 0 1 0 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 0 0 1 1 0
0 0 1 0 0 1 1 1 1 1 0 1 1 1 0 0 0 1 0 1 0 1 1 1
0 0 1 0 1 0 0 0 1 1 1 1 1 1 0 1 0 1 0 1 1 0 0 0
0 0 1 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 1 0 0 1
0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0
0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1
0 0 1 0 1 1 0 0 1 0 1 0 1 0 0 1 0 1 0 0 1 1 0 0
0 0 1 0 1 1 0 1 1 0 0 1 1 0 0 0 0 1 0 1 1 1 0 1
0 0 1 0 1 1 1 0 0 1 1 1 0 1 0 1 0 1 0 1 1 1 1 0
0 0 1 0 1 1 1 1 0 1 0 0 0 1 0 0 0 1 0 1 1 1 1 1

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0 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0
0 0 1 1 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 0 0 1
0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 1 1 0 0 1 0
0 0 1 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1
0 0 1 1 0 1 0 0 1 1 0 1 1 1 0 0 0 1 1 1 0 1 0 0
0 0 1 1 0 1 0 1 1 1 1 0 1 1 0 1 0 1 1 0 0 1 0 1
0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0
0 0 1 1 0 1 1 1 0 0 1 1 0 0 0 1 0 1 1 1 0 1 1 1
0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 0
0 0 1 1 1 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 0 0 1
0 0 1 1 1 0 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 1 0
0 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 1 1
0 0 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 0
0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 1
0 0 1 1 1 1 1 0 1 0 0 1 1 0 0 0 0 1 1 1 1 1 1 0
0 0 1 1 1 1 1 1 1 0 1 0 1 0 0 1 0 1 1 0 1 1 1 1
0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1
0 1 0 0 0 0 1 0 0 1 1 1 0 1 0 1 1 0 0 1 0 0 1 0
0 1 0 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1
0 1 0 0 0 1 0 0 1 1 1 1 1 1 0 1 1 0 0 1 0 1 0 0
0 1 0 0 0 1 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 1 0 1
0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 0
0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 0 0 1 0 1 1 1
0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 1 1 0 0 0
0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1
0 1 0 0 1 0 1 0 1 1 1 0 1 1 0 1 1 0 0 0 1 0 1 0
0 1 0 0 1 0 1 1 1 1 0 1 1 1 0 0 1 0 0 1 1 0 1 1
0 1 0 0 1 1 0 0 0 1 1 0 0 1 0 1 1 0 0 0 1 1 0 0
0 1 0 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0 1 1 1 0 1
0 1 0 0 1 1 1 0 1 0 1 1 1 0 0 1 1 0 0 1 1 1 1 0
0 1 0 0 1 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1
0 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 0 0
0 1 0 1 0 0 0 1 0 1 1 1 0 1 0 1 1 0 1 1 0 0 0 1
0 1 0 1 0 0 1 0 1 0 0 1 1 0 0 0 1 0 1 1 0 0 1 0
0 1 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1 0 1 0 0 0 1 1
0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 0 0
0 1 0 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 0 0 1 0 1
0 1 0 1 0 1 1 0 1 1 0 0 1 1 0 0 1 0 1 0 0 1 1 0

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0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1
0 1 0 1 1 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 0 0
0 1 0 1 1 0 0 1 1 1 1 0 1 1 0 1 1 0 1 0 1 0 0 1
0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0
0 1 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 1 0 1 1
0 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 1 0 1 0 1 1 0 0
0 1 0 1 1 1 0 1 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 1
0 1 0 1 1 1 1 0 0 1 0 1 0 1 0 0 1 0 1 1 1 1 1 0
0 1 0 1 1 1 1 1 0 1 1 0 0 1 0 1 1 0 1 0 1 1 1 1
0 1 1 0 0 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0
0 1 1 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 0 1 0 0 0 1
0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 0
0 1 1 0 0 0 1 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 1
0 1 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 1 0 0
0 1 1 0 0 1 0 1 1 0 1 0 1 0 0 1 1 1 0 0 0 1 0 1
0 1 1 0 0 1 1 0 0 1 0 0 0 1 0 0 1 1 0 0 0 1 1 0
0 1 1 0 0 1 1 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1
0 1 1 0 1 0 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 0 0 0
0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1
0 1 1 0 1 0 1 0 1 0 0 0 1 0 0 0 1 1 0 0 1 0 1 0
0 1 1 0 1 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 0 1 1
0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0
0 1 1 0 1 1 0 1 0 0 1 1 0 0 0 1 1 1 0 1 1 1 0 1
0 1 1 0 1 1 1 0 1 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0
0 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 1 1
0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0
0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 1
0 1 1 1 0 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 0
0 1 1 1 0 0 1 1 1 1 0 0 1 1 0 0 1 1 1 0 0 0 1 1
0 1 1 1 0 1 0 0 0 1 1 1 0 1 0 1 1 1 1 1 0 1 0 0
0 1 1 1 0 1 0 1 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 1
0 1 1 1 0 1 1 0 1 0 1 0 1 0 0 1 1 1 1 0 0 1 1 0
0 1 1 1 0 1 1 1 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 1
0 1 1 1 1 0 0 0 1 0 1 1 1 0 0 1 1 1 1 1 1 0 0 0
0 1 1 1 1 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 1 0 0 1
0 1 1 1 1 0 1 0 0 1 1 0 0 1 0 1 1 1 1 0 1 0 1 0
0 1 1 1 1 0 1 1 0 1 0 1 0 1 0 0 1 1 1 1 1 0 1 1
0 1 1 1 1 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 1 1 0 0
0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 0 1

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0 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 1 0
0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1
1 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 1
1 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0
1 0 0 0 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1 1
1 0 0 0 0 1 0 0 1 0 0 1 1 0 1 0 0 0 0 1 0 1 0 0
1 0 0 0 0 1 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 1 0 1
1 0 0 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1 1 0
1 0 0 0 0 1 1 1 0 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1
1 0 0 0 1 0 0 0 0 1 0 1 0 1 1 0 0 0 0 1 1 0 0 0
1 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 0 0 0 0 1 0 0 1
1 0 0 0 1 0 1 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0
1 0 0 0 1 0 1 1 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1
1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0
1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 1 0 0 0 1 1 1 0 1
1 0 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 0 1 1 1 1 0
1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 1 1
1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0
1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 1
1 0 0 1 0 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1 0
1 0 0 1 0 0 1 1 1 1 0 0 1 1 1 0 0 0 1 0 0 0 1 1
1 0 0 1 0 1 0 0 0 1 1 1 0 1 1 1 0 0 1 1 0 1 0 0
1 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 0 1
1 0 0 1 0 1 1 0 1 0 1 0 1 0 1 1 0 0 1 0 0 1 1 0
1 0 0 1 0 1 1 1 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 1
1 0 0 1 1 0 0 0 1 0 1 1 1 0 1 1 0 0 1 1 1 0 0 0
1 0 0 1 1 0 0 1 1 0 0 0 1 0 1 0 0 0 1 0 1 0 0 1
1 0 0 1 1 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 1 0 1 0
1 0 0 1 1 0 1 1 0 1 0 1 0 1 1 0 0 0 1 1 1 0 1 1
1 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 0 0 1 0 1 1 0 0
1 0 0 1 1 1 0 1 1 1 0 1 1 1 1 0 0 0 1 1 1 1 0 1
1 0 0 1 1 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 1 1 1 0
1 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1
1 0 1 0 0 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 0 0 0 0
1 0 1 0 0 0 0 1 1 0 0 1 1 0 1 0 0 1 0 1 0 0 0 1
1 0 1 0 0 0 1 0 0 1 1 1 0 1 1 1 0 1 0 1 0 0 1 0
1 0 1 0 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 0 1 1
1 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 0

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1 0 1 0 0 1 0 1 1 1 0 0 1 1 1 0 0 1 0 0 0 1 0 1
1 0 1 0 0 1 1 0 0 0 1 0 0 0 1 1 0 1 0 0 0 1 1 0
1 0 1 0 0 1 1 1 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 1
1 0 1 0 1 0 0 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 0 0
1 0 1 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 1
1 0 1 0 1 0 1 0 1 1 1 0 1 1 1 1 0 1 0 0 1 0 1 0
1 0 1 0 1 0 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 1
1 0 1 0 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 0 0
1 0 1 0 1 1 0 1 0 1 0 1 0 1 1 0 0 1 0 1 1 1 0 1
1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0
1 0 1 0 1 1 1 1 1 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1
1 0 1 1 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 0 0 0
1 0 1 1 0 0 0 1 0 1 1 1 0 1 1 1 0 1 1 1 0 0 0 1
1 0 1 1 0 0 1 0 1 0 0 1 1 0 1 0 0 1 1 1 0 0 1 0
1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 0 1 1 0 0 0 1 1
1 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 0 0
1 0 1 1 0 1 0 1 0 0 1 0 0 0 1 1 0 1 1 0 0 1 0 1
1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0
1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1
1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 0 1 1 1 1 0 0 0
1 0 1 1 1 0 0 1 1 1 1 0 1 1 1 1 0 1 1 0 1 0 0 1
1 0 1 1 1 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 0
1 0 1 1 1 0 1 1 0 0 1 0 0 0 1 1 0 1 1 1 1 0 1 1
1 0 1 1 1 1 0 0 1 0 0 0 1 0 1 0 0 1 1 0 1 1 0 0
1 0 1 1 1 1 0 1 1 0 1 0 1 0 1 1 0 1 1 1 1 1 0 1
1 0 1 1 1 1 1 0 0 1 0 0 0 1 1 0 0 1 1 1 1 1 1 0
1 0 1 1 1 1 1 1 0 1 1 0 0 1 1 1 0 1 1 0 1 1 1 1
1 1 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0
1 1 0 0 0 0 0 1 0 1 0 0 0 1 1 0 1 0 0 1 0 0 0 1
1 1 0 0 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 1 0 0 1 0
1 1 0 0 0 0 1 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1
1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0
1 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1
1 1 0 0 0 1 1 0 1 1 1 0 1 1 1 1 1 0 0 0 0 1 1 0
1 1 0 0 0 1 1 1 1 1 0 0 1 1 1 0 1 0 0 1 0 1 1 1
1 1 0 0 1 0 0 0 1 1 1 0 1 1 1 1 1 0 0 1 1 0 0 0
1 1 0 0 1 0 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 0 0 1
1 1 0 0 1 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 1 0
1 1 0 0 1 0 1 1 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1

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1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 0 1 1 0 0
1 1 0 0 1 1 0 1 1 0 0 0 1 0 1 0 1 0 0 1 1 1 0 1
1 1 0 0 1 1 1 0 0 1 1 0 0 1 1 1 1 0 0 1 1 1 1 0
1 1 0 0 1 1 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 1 1 1
1 1 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0
1 1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1
1 1 0 1 0 0 1 0 0 1 0 0 0 1 1 0 1 0 1 1 0 0 1 0
1 1 0 1 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 0 0 1 1
1 1 0 1 0 1 0 0 1 1 0 0 1 1 1 0 1 0 1 1 0 1 0 0
1 1 0 1 0 1 0 1 1 1 1 0 1 1 1 1 1 0 1 0 0 1 0 1
1 1 0 1 0 1 1 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 1 0
1 1 0 1 0 1 1 1 0 0 1 0 0 0 1 1 1 0 1 1 0 1 1 1
1 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0
1 1 0 1 1 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 1
1 1 0 1 1 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 0 1 0
1 1 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1
1 1 0 1 1 1 0 0 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0
1 1 0 1 1 1 0 1 0 1 1 0 0 1 1 1 1 0 1 1 1 1 0 1
1 1 0 1 1 1 1 0 1 0 0 0 1 0 1 0 1 0 1 1 1 1 1 0
1 1 0 1 1 1 1 1 1 0 1 0 1 0 1 1 1 0 1 0 1 1 1 1
1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0
1 1 1 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 1 0 0 0 1
1 1 1 0 0 0 1 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 0
1 1 1 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 1 1
1 1 1 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 1 0 1 0 0
1 1 1 0 0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 0 1
1 1 1 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0
1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 1 1 1
1 1 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0
1 1 1 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 0 0 1
1 1 1 0 1 0 1 0 0 1 0 0 0 1 1 0 1 1 0 0 1 0 1 0
1 1 1 0 1 0 1 1 0 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1
1 1 1 0 1 1 0 0 1 1 0 0 1 1 1 0 1 1 0 0 1 1 0 0
1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 1
1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 1 0
1 1 1 0 1 1 1 1 0 0 1 0 0 0 1 1 1 1 0 0 1 1 1 1
1 1 1 1 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0
1 1 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 0 0 0 1
1 1 1 1 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1 1 0 0 1 0

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1 1 1 1 0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 1
1 1 1 1 0 1 0 0 1 0 1 0 1 0 1 1 1 1 1 1 0 1 0 0
1 1 1 1 0 1 0 1 1 0 0 0 1 0 1 0 1 1 1 0 0 1 0 1
1 1 1 1 0 1 1 0 0 1 1 0 0 1 1 1 1 1 1 0 0 1 1 0
1 1 1 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 1 1 1
1 1 1 1 1 0 0 0 0 1 1 0 0 1 1 1 1 1 1 1 1 0 0 0
1 1 1 1 1 0 0 1 0 1 0 0 0 1 1 0 1 1 1 0 1 0 0 1
1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 1 1 1 1 0 1 0 1 0
1 1 1 1 1 0 1 1 1 0 0 0 1 0 1 0 1 1 1 1 1 0 1 1
1 1 1 1 1 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 1 1 0 0
1 1 1 1 1 1 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 1
1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0
1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 1

Example:

To transmit the data

1 0 1 1 1 0 0 1
D7 D6 D5 D4 D3 D2 D1 D0

Put the data switches as

OFF

ON

Calculated parity bits

P3 : D7+D6+D4+D3+D1
: 1+0+1+1+0=1
P2 : D7+D5+D4+D2+D1
: 1+1+1+0+0=1
P1 : D6+D5+D4+D0
: 0+1+1+1=1
P0 : D3+D2+D1+D0
: 1+0+0+1=0

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Complete data frame : T11 T10 T9 T8 T7 T6 T5 T4 T3 T2 T1 T0

: 111101101001

4.We can check the Tx data and Data clk on the DSO or CRO, and also can change the Data
frequency by the Frequency selector switch.

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Experiment No:-4(B)

Aim:-To Generate error in Transmitted Hamming Data Frame.

Equipment Required:- EDAC Techniques Trainer Kit, CRO/DSO, Power Cord.

Theory:-
During the transmission process, the signal passes through some noisy channels .Due to noise
interference some errors are introduced in the received data. These errors can be detected and
sometimes corrected using coding techniques. Coding techniques add some extra bits to the
message bits and these bits are used to detect errors at the receiver. Although these extra bits
reduce the bit rate of transmitter and its power, but the advantage is that error probability is
reduced

Generally the error control methods are of 2 types

1.Error detection:
In this method, when the errors are detected at the reciever the retransmission signal is sent
back to the transmitter.

2.Error detection and correction:

In this method the errors are detected and corrected by proper coding techniques at the receiver
end. In this experiment parity coding is used for error detection only & hamming code is used
for single bit error correction.
In this kit there are 8 data inputs i.e. D0-D7 and four parity bits i.e P0-P3 respectively. It has
eight error generator switches i.e. E0-E7.

Procedure:-
1.Connect the power cord and Switch on the Experiment kit.
2.First insert the selected data using the data switches i.e. D0-D7.

Example:

To transmit the data

1 0 1 1 1 0 0 1
D7 D6 D5 D4 D3 D2 D1 D0

Put the data switches as

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OFF

ON

Calculated parity bits

P3 : D7+D6+D4+D3+D1
: 1+0+1+1+0=1
P2 : D7+D5+D4+D2+D1
: 1+1+1+0+0=1
P1 : D6+D5+D4+D0
: 0+1+1+1=1
P0 : D3+D2+D1+D0
: 0+1+1+0=0

Data frame without error : T11 T10 T9 T8 T7 T6 T5 T4 T3 T2 T1 T0

: 111101101001

Put the error switch

0 0 0 0 0 0 1 0
E7 E6 E5 E4 E3 E2 E1 E0

OFF

ON

Data frame with error : T11 T10 T9 T8 T7 T6 T5 T4 T3 T2 T1 T0

: 111101101000

3. We can check the Tx data and Data clk on the DSO or CRO, and also can change the Data
frequency by the Frequency selector switch.

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Experiment No:-4(C)

Aim:-To Correct Error in Transmitted Hamming Data Frame.

Equipment Required:- EDAC Techniques Trainer Kit, CRO/DSO, connecting Probes,

Power Cord.

Theory:-
Hamming Codes are used in detecting and correcting a code. An error-correcting code is an
algorithm for expressing a sequence of numbers such that any errors which are introduced can be
detected and corrected (within certain limitations) based on the remaining numbers. Errors can
happen in a variety of ways. Bits can be added, deleted, or flipped. Errors can happen in fixed or
variable codes.
In this kit there are 8 data inputs i.e. D0-D7 and four parity bits i.e P0-P3 respectively. It has
eight error generator switches i.e. E0-E7 and at the receiver side four decoding bits i.e. C0-C3
which is used to decode the error location, these bits are used to decide the location of the error
bit.

Procedure:-
1.Switch on the Experiment kit.
2.Hamming code technique used in this kit is a (8,4) which means there are four hamming code
parity bits.
3.First insert the selected data using the data switches i.e. D0-D7.

Example:

To transmit the data

1 0 1 1 1 0 0 1
D7 D6 D5 D4 D3 D2 D1 D0

Put the data switches as

OFF

ON

Calculated parity bits : P3= D7+D6+D4+D3+D1

1+0+1+1+0=1
P2= D7+D5+D4+D2+D1

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1+1+1+0+0=1
P1= D6+D5+D4+D0
0+1+1+1=1
P0= D3+D2+D1+D0
1 + 0 + 0 + 1= 0

Data frame without error : T11 T10 T9 T8 T7 T6 T5 T4 T3 T2 T1 T0

: 111101101001
Put the error switch

0 0 0 0 0 0 1 0
E7 E6 E5 E4 E3 E2 E1 E0

OFF

ON

Hamming decoding bits : C3 C2 C1 C0

: 1011

The binary equivalent of 1011 is 11 it means the error is in the 11th bit.

Data frame with error : T11 T10 T9 T8 T7 T6 T5 T4 T3 T2 T1 T0

: 111101101011

4.The error indicator red light will glow when error is generated.
5.Check the wave form of the transmitted data at Tx test point using CRO.
6.The hamming decoding bit is successfully calculated in the received hamming data frame.

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Experiment No:-4(D)

Aim:-To Transmit 8 bit binary data using Hamming Encoding & Decoding Technique without
Error.

Equipment Required:-Hamming kit, CRO, Connecting probes, Power supply.

Theory:-
Hamming Codes are used in detecting and correcting a code. An error-correcting code is an
algorithm for expressing a sequence of numbers such that any errors which are introduced can be
detected and corrected (within certain limitations) based on the remaining numbers. Errors can
happen in a variety of ways. Bits can be added, deleted, or flipped. Errors can happen in fixed or
variable codes.
In this kit there are 8 data inputs i.e. D0-D7 and four parity bits i.e P0-P3 respectively. It has
eight error generator switches i.e. E0-E7 and at the receiver side four decoding bits i.e. C0-C3
which is used to decode the error location, these bits are used to decide the location of the error
bit. There are eight bits i.e. E’0-E’7 which is used to indicate the error bit, in which bit the error
is generated.

Procedure:-
1.Switch on the Experiment kit.
2.Hamming code technique used in this kit is a (8,4) which means there are four hamming code
parity bits.
3.First insert the selected data using the data switches i.e. D0-D7.

Example:

To transmit the data

1 0 1 1 1 0 0 1
D7 D6 D5 D4 D3 D2 D1 D0

Put the data switches as

OFF

ON

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Calculated parity bits : P3= D7+D6+D4+D3+D1

1+0+1+1+0=1
P2= D7+D5+D4+D2+D1
1+1+1+0+0=1
P1= D6+D5+D4+D0
0+1+1+1=1
P0= D3+D2+D1+D0
1+0+0+1=0

Data frame without error : T11 T10 T9 T8 T7 T6 T5 T4 T3 T2 T1 T0

: 111101101001

4. In this the green led of the error indicator will glow because there is no error in the transmitted
data.
5.Check the waveform of the transmitted data at Tx test point and received data at Rx test point
using CRO.
6.The 8 bit binary data is successfully transmitted using hamming encoding & decoding
technique without any error.
WAVEFORMS:-

FIG.4(D)1: : SERIAL DATA TX AND DATA CLOCK WITHOUT ERROR

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Experiment No:-4(E)
Aim:-To transmit 8 bit binary data using hamming encoding & decoding technique with an
error.

Equipment Required:-Hamming kit, CRO, Connecting probes, Power supply.

Theory:-
Hamming Codes are used in detecting and correcting a code. An error-correcting code is an
algorithm for expressing a sequence of numbers such that any errors which are introduced can be
detected and corrected (within certain limitations) based on the remaining numbers. Errors can
happen in a variety of ways. Bits can be added, deleted, or flipped. Errors can happen in fixed or
variable codes.
Generally the error control methods are of 2 types

1.Error detection:
In this method, when the errors are detected at the receiver the retransmission signal is sent
back to the transmitter.
2.Error detection and correction:
In this method the errors are detected and corrected by proper coding techniques at the receiver
end. In this experiment parity coding is used for error detection only & hamming code is used
for single bit error correction.
In this kit there are 8 data inputs i.e. D0-D7 and four parity bits i.e. P0-P3 respectively. It has
eight error generator switches i.e. E0-E7 and at the receiver side four decoding bits i.e. C0-C3
which is used to decode the error location, these bits are used to decide the location of the error
bit. There are eight bits i.e. E’0-E’7 which is used to indicate the error bit, in which bit the error
is generated.
Procedure:-
5.Switch on the Experiment kit.
6.Hamming code technique used in this kit is a (8,4) which means there are four hamming code
parity bits.
7.First insert the selected data using the data switches i.e. D0-D7.

Example:

To transmit the data

1 0 1 1 1 0 0 1
D7 D6 D5 D4 D3 D2 D1 D0

Put the data switches as

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OFF

ON

Calculated parity bits : P3= D7+D6+D4+D3+D1

1+0+1+1+0=1
P2= D7+D5+D4+D2+D1
: 1+1+1+0+0=1
P1= D6+D5+D4+D0
: 0+1+1+1=1
P0= D3+D2+D1+D0
: 1+0+0+1=0
Put the error switch

0 0 0 0 0 0 1 0
E7 E6 E5 E4 E3 E2 E1 E0

OFF

ON

Hamming decoding bits : C3 C2 C1 C0

: 1011

The binary equivalent of 1011 is 11 it means the error is in the 11th bit.

Data frame with error : T11 T10 T9 T8 T7 T6 T5 T4 T3 T2 T1 T0

: 111101101011

8.The error indicator red light will glow when error is generated.

Corrected output data : D’7 D’6 D’5 D’4 D’3 D’2 D’1 D’0

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: 10111001

9.The 8 bit binary data is successfully transmitted by using hamming encoding & decoding
technique with an error.

WAVEFORMS:-

FIG.4(E)1: : SERIAL DATA TX AND DATA CLOCK WITH ERROR IN D(1)

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