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how to create barcode in microsoft excel 2007 SECTION 102 in Software
SECTION 102 Code39 Drawer In None Using Barcode generator for Software Control to generate, create Code 39 Extended image in Software applications. ANSI/AIM Code 39 Decoder In None Using Barcode reader for Software Control to read, scan read, scan image in Software applications. BLOCK CODING
ANSI/AIM Code 39 Drawer In C#.NET Using Barcode maker for Visual Studio .NET Control to generate, create Code 39 image in VS .NET applications. Code 39 Encoder In Visual Studio .NET Using Barcode generation for ASP.NET Control to generate, create Code 3 of 9 image in ASP.NET applications. Notice particularly that addition and subtraction give the same results In this arithmetic we use the XOR (exclusive OR) operation for both addition and subtraction The result of an XOR operation is 0 if two bits are the same; the result is I if two bits are different Figure 104 shows this operation Encoding USS Code 39 In .NET Framework Using Barcode generation for .NET framework Control to generate, create Code39 image in Visual Studio .NET applications. Code39 Creation In VB.NET Using Barcode maker for .NET Control to generate, create Code39 image in VS .NET applications. Figure 104 XORing of two single bits or two words
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Paint Matrix Barcode In C#.NET Using Barcode generation for .NET Control to generate, create 2D Barcode image in VS .NET applications. Code 39 Generator In Java Using Barcode creation for Java Control to generate, create Code 39 image in Java applications. Other Modulo Arithmetic
UPCA Supplement 2 Creation In None Using Barcode generator for Excel Control to generate, create UPC Symbol image in Microsoft Excel applications. GS1 128 Generation In Java Using Barcode generator for Java Control to generate, create EAN / UCC  13 image in Java applications. We also use, moduloN arithmetic through the book The principle is the same; we use numbers between 0 and N  1 If the modulus is not 2, addition and subtraction are distinct If we get a negative result, we add enough multiples of N to make it positive BLOCK CODING
In block coding, we divide our message into blocks, each of k bits, called datawords We add r redundant bits to each block to make the length n = k + r The resulting nbit blocks are called codewords How the extra r bits is chosen or calculated is something we will discuss later For the moment, it is important to know that we have a set of datawords, each of size k, and a set of codewords, each of size of n With k bits, we can create a combination of 2k datawords; with n bits, we can create a combination of 2n codewords Since n > k, the number of possible codewords is larger than the number of possible datawords The block coding process is onetoone; the same dataword is always encoded as the same codeword This means that we have 2n  2k codewords that are not used We call these codewords invalid or illegal Figure 105 shows the situation Figure 105 Datawords and codewords in block coding
Hits
Hits
I Hits I
2k Datawords, each of k bits
bits
bits
nbits
2n Codewords, each of n bits (only 2k of them are valid) ERROR DETECTION AND CORRECTION
Example 101
The 4B/5B block coding discussed in 4 is a good example of this type of coding In this coding scheme, k = 4 and n = 5 As we saw, we have 2k = 16 datawords and 2n = 32 codewords We saw that 16 out of 32 codewords are used for message transfer and the rest are either used for other purposes or unused Error Detection
How can errors be detected by using block coding If the following two conditions are met, the receiver can detect a change in the original codeword 1 The receiver has (or can find) a list of valid codewords 2 The original codeword has changed to an invalid one Figure 106 shows the role of block coding in error detection Figure 106 Process of error detection in block coding
Sender Encoder
k bits I D,at:aword 1
Receiver Decoder
I Dat~~ord 1
k bits
I Generator I
n bits I
Codeword
Extract Discard
I Checker
Unreliable transmission
r Codeword r
In bits
The sender creates codewords out of datawords by using a generator that applies the rules and procedures of encoding (discussed later) Each codeword sent to the receiver may change during transmission If the received codeword is the same as one of the valid codewords, the word is accepted; the corresponding dataword is extracted for use If the received codeword is not valid, it is discarded However, if the codeword is corrupted during transmission but the received word still matches a valid codeword, the error remains undetected This type of coding can detect only single errors Two or more errors may remain undetected Example 102
Let us assume that k = 2 and n = 3 Table 101 shows the list of datawords and codewords Later, we will see how to derive a codeword from a dataword Table 101 A code for error detection (Example 102) Datawords 00 01 10 11 Codewords 000
SECTION 102
BLOCK CODING
Assume the sender encodes the dataword 01 as 011 and sends it to the receiver Consider the following cases: 1 The receiver receives OIl It is a valid codeword The receiver extracts the dataword 01
from it 2 The codeword is corrupted during transmission, and 111 is received (the leftmost bit is corrupted) This is not a valid codeword and is discarded 3 The codeword is corrupted during transmission, and 000 is received (the right two bits are corrupted) This is a valid codeword The receiver incorrectly extracts the dataword 00 Two corrupted bits have made the error undetectable An errordetecting code can detect only the types of errors for which it is designed; other types of errors may remain undetected

