ARITHMETIC OPERATIONS in VS .NET Drawing Quick Response Code in VS .NET ARITHMETIC OPERATIONS 16.2 ARITHMETIC OPERATIONSRecognize Quick Response Code In Visual Studio .NETUsing Barcode Control SDK for VS .NET Control to generate, create, read, scan barcode image in .NET applications.TABLE 16.1 operation 0 0 0 0 1 1 1 1 sign1 0 0 1 1 0 0 1 1 sign2 0 1 0 1 0 1 0 1 actual operation s1 s2 s1 2 s2 2(s1 2 s2) 2(s1 s2) s1 2 s2 s1 s2 2(s1 s2) 2(s1 2 s2)QR-Code Generator In .NETUsing Barcode maker for .NET framework Control to generate, create Quick Response Code image in Visual Studio .NET applications.Once the signi cands have been aligned, the actual operation (addition or subtraction of the signi cands) depends on the values of operation, sign1, and sign2 (Table 16.1). The following algorithm, based on Algorithms 16.1 and 16.2 as well as Table 16.1, computes z. Algorithm 16.3 Addition and SubtractionQR Code Scanner In VS .NETUsing Barcode decoder for .NET Control to read, scan read, scan image in Visual Studio .NET applications.if e1>=e2 then e:=e1; s2:=s2/B**(e1-e2); else e:=e2; s1:=s1/B**(e2-e1); end if; sign:=sign1; if operation xor sign1 xor sign2=0 then s:=s1+s2; if s>=B then e:=e+1; s:=s/B; end if; s:=round(s); if s>=B then e:=e+1; s:=s/B; end if; else s:=s1-s2; if s<0 then s:=-s; sign:=1-sign; end if; leading_zeroes(s, k); s:=s*(B**k); e:=e-k; s:=round(s); if s>=B then e:=e+1; s:=s/B; end if; end if;Bar Code Printer In VS .NETUsing Barcode creator for VS .NET Control to generate, create bar code image in Visual Studio .NET applications.As regards the hardware implementation, the following equivalent algorithm is better. Algorithm 16.4 Addition and Subtraction, Second VersionReading Bar Code In .NET FrameworkUsing Barcode reader for .NET Control to read, scan read, scan image in Visual Studio .NET applications.if operation=1 then sign2:=1-sign2; end if; if e1=B then e:=e+1; s:=s/B; end if; else if (e1=e2) and (s1=B then e:=e+1; s:=s/B; end if;Make QR-Code In Visual Basic .NETUsing Barcode generation for Visual Studio .NET Control to generate, create QR Code image in .NET framework applications.Multiplication EAN / UCC - 13 Generator In .NET FrameworkUsing Barcode creation for VS .NET Control to generate, create EAN / UCC - 13 image in Visual Studio .NET applications.Given two oating-point numbers (21)sign1.s1.Be1 and (21)sign2.s2.Be2, their product (21)sign.s.Be is computed as follows: sign sign1 xor sign2 , The value of s belongs to the interval 1 s (B ulp)2 , (16:15) s s1 :s2 , e e1 e2 : (16:14)Painting Data Matrix ECC200 In VS .NETUsing Barcode printer for .NET Control to generate, create Data Matrix image in Visual Studio .NET applications.and could be greater than or equal to B. If it is the case, that is, if B s (B ulp)2 , (16:16)Code 128A Printer In .NET FrameworkUsing Barcode creation for VS .NET Control to generate, create Code 128A image in VS .NET applications.then (normalization) substitute s by s/B, and e by e 1. The new value of s satis es 1 s (B ulp)2 =B B 2:ulp (ulp)2 =B , B ulp (16:17)Printing EAN 8 In .NET FrameworkUsing Barcode maker for .NET framework Control to generate, create EAN 8 image in Visual Studio .NET applications.(ulp , B so that 2 2 ulp/B . 1). It remains to round the signi cand and to normalize if necessary. Making UPC-A Supplement 5 In C#Using Barcode printer for .NET Control to generate, create UPC Code image in Visual Studio .NET applications.Algorithm 16.5 Encode ECC200 In Visual Studio .NETUsing Barcode maker for ASP.NET Control to generate, create Data Matrix ECC200 image in ASP.NET applications.Multiplication Code 39 Encoder In Visual Basic .NETUsing Barcode drawer for .NET framework Control to generate, create Code 39 image in VS .NET applications.sign:=sign1 xor sign2; s:=s1*s2; e:=e1+e2; if s>=B then e:=e+1; s:=s/B; end if; s:=round(s); if s>=B then e:=e+1; s:=s/B; end if;Make Code 128 Code Set B In Visual C#.NETUsing Barcode generation for Visual Studio .NET Control to generate, create Code 128A image in .NET framework applications.Examples 16.4 Assume that B 10 and ulp 1024, so that the numbers are represented in the form s.10e, where 1 s 9.9999.Data Matrix ECC200 Creator In JavaUsing Barcode creator for Java Control to generate, create Data Matrix image in Java applications.16.2 ARITHMETIC OPERATIONS GTIN - 13 Drawer In JavaUsing Barcode generator for Java Control to generate, create EAN 13 image in Java applications.1. Compute z (3.4382 103) (2.5471 1021): z 8:75743922 102 , 8:75743922 , 10, rounding: s 8:7574, 8:7574 , 10, z 8:7574 10 2 : 2. Compute z (9.4300 103) (8.6200 102): z 81:2866 105 , normalization: s 8:12866, rounding: s 8:1287, 8:1287 , 10, z 8:1287 106 : 3. Compute z (4.7619 102) (2.1000 103): z 9:99999 105 , 9:99999 , 10, rounding: s 10:00, normalization: s 1, e 6, z 1:0000 106 : Comment 16.3 The product of two real numbers could produce an over ow as the nal value of e could be greater than emax. 16.2.5 Division Given two oating-point numbers (21)sign1.s1.Be1 and (21)sign2.s2.Be2 their quotient (21)sign.s.Be is computed as follows: sign sign1 xor sign2 , The value of s belongs to the interval 1=B , s B ulp, (16:19) s s1 =s2 , e e1 e2 (16:18) e 6,Code-128 Maker In VB.NETUsing Barcode printer for Visual Studio .NET Control to generate, create Code 128 Code Set A image in VS .NET applications.and could be smaller than 1. If that is the case, that is if s s1/s2 , 1, then s1 , s2 , and 1=B , s , 1 ulp=B: (16:20) s1 s2 ulp, s1 =s2 1 ulp=s2 , 1 ulp=B,Code 39 Drawer In JavaUsing Barcode generator for Java Control to generate, create Code 39 Extended image in Java applications.FLOATING-POINT UNIT Then (normalization) substitute s by s.B, and e by e 2 1. The new value of s satis es 1 , s , B ulp It remains to round the signi cand. Algorithm 16.6 Division (16:21)sign:=sign1 xor sign2; s:=s1/s2; e:=e1 2 e2; if s<1 then e:=e21; s:=s*B; end if; s:=round(s);Examples 16.5 Assume that B 10 and ulp 1024, so that the numbers are represented in the form s.10e, where 1 s 9.9999. 1. Compute z (3.4375 103)/(2.5491 1021): z 1:3485152 102 , 1:3485152 ! 1, rounding: s 1:3485, z 1:3485 102 : 2. Compute z (2.5491 1021)/(3.4375 103): z 0:74155564 10 4 , normalization: s 7:4155564, e 5, rounding: s 7:4156, z 7:4156 10 5 : Comment 16.4 The quotient of two real numbers could produce an under ow, as the nal value of e could be smaller than emin. 16.2.6 Square RootGiven a positive oating-point number s1.Be1, its square root s.Be is computed as follows: if e1 is even, if e1 is odd, In the rst case (16.22), 1 s (B ulp)1=2 , B ulp: (16:24) s (s1 )1=2 , e e1 =2; s (s1 =B)1=2 , e (e1 1)=2: (16:22) (16:23)