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ARITHMETIC in .NET Creation barcode pdf417 in .NET ARITHMETIC




How to generate, print barcode using .NET, Java sdk library control with example project source code free download:
ARITHMETIC use .net vs 2010 pdf 417 integrated todraw barcode pdf417 with .net Microsoft .NET Compact Framework tain the results. S pdf417 for .NET ubtraction requires each residue digit of the subtrahend to be complemented with respect to its modulus before performing addition.

Addition and multiplication examples are shown in Figure 3-26. For these examples, the. 29 + 27 = 56 Decimal 29 27 56 Figure 3-26. 10 17 = 170 Decimal 10 17 170 Residue 5794 0312 2381 0282 Residue 5794 4121 2603 1020 Examples of addition and multiplication in the residue number system. moduli used are 5, Visual Studio .NET pdf417 2d barcode 7, 9, and 4. Addition is performed in parallel for each column, with no carry propagation.

Multiplication is also performed in parallel for each column, independent of the other columns. Although residue arithmetic operations can be very fast, there are a number of disadvantages to the system. Division and sign detection are dif cult, and a representation for fractions is also dif cult.

Conversions between the residue number system and weighted number systems are complex, and often require involved methods such as the Chinese remainder theorem. The conversion problem is important because the residue number system is not very useful without being translated to a weighted number system so that magnitude comparisons can be made. However, for integer applications in which the time spent in addition, subtraction, and multiplication outweighs the time spent in division, conversion, etc.

, the residue number system may be a practical approach. An important application area is matrix-vector multiplication, which is used extensively in signal processing..

EXAMPLE: WIDE WORD HIGH PERFORMANCE ADDER A practical word wi PDF 417 for .NET dth for a carry lookahead adder (CLA) is four bits, whereas a 16-bit word width is not as practical because of the large fan-ins and fan-outs of the internal logic. We can subdivide a 16-bit addition problem into four 4-bit groups in which carry lookahead is used within the groups, and in which carry lookahead is also used among the groups.

This organization is referred to as a group carry lookahead adder (GCLA). For this example, we will compare a. ARITHMETIC 16-bit CLA with a 1 PDF417 for .NET 6-bit GCLA in terms of gate delays, fan-ins, and fan-outs. Figure 3-27 shows a 16-bit GCLA that is composed of four 4-bit CLAs, with.

a12 a15 b12 b15 4 4 c12 a8 a11 b8 b11 4 4 c8 a4 a7 b4 b7 4 4 c4 a0 a3 b0 b3 4 4 c0 CLA3 4 s12 s15 GP3 GG3 GP2 CLA2 4 s8 s11 GG2 GP1 CLA1 4 s4 s 7 GG1 GP0 CLA0 4 s0 s 3 GG0. Figure 3-27. Group Carry Lookahead Logic A 16-bit group carry lookahead adder. some additional log ic that generates the carries between the four-bit groups. Each group behaves as an ordinary CLA, except that the least signi cant carry into each CLA is treated as a variable instead of as a 0, and that group generate (GG) and group propagate (GP) signals are generated. A GG signal is generated when a carry is generated somewhere within a group, and all of the more signi cant propagate signals are true.

This means that a carry into a group will propagate all the way through the group. The corresponding equations for the least signi cant GG and GP signals in Figure 3-27 are shown below: GG0 = G3 + P3G2 + P3P2G1 + P3P2P1G0 GP0 = P3P2P1P0 The remaining GG and GP signals are computed similarly. The carry into each group, except for the carry into CLA0, is computed from the GG and GP signals.

For example, c4 is true when GG0 is true or when GP0 and c0 are both true. The corresponding equation is: c4 = GG0 + GP0c0..

ARITHMETIC Higher order carrie s out of each group are computed in a similar manner: c8 = GG1 + GP1c4 = GG1 + GP1GG0 + GP1GP0c0. c12 = GG2 + GP2c8 = GG2 + GP2GG1 + GP2GP1GG0 + GP2GP1GP0c0. c16 = GG3 + GP3c12 = GG3 + GP3GG2 + GP3GP2GG1 + GP3GP2GP1GG0 + GP3GP2GP1GP0c0.

In terms of gate delays, a 16-bit CLA has a longest path of ve gate delays to produce the most signi cant sum bit, as discussed in Section 3.5.1.

Each of the CLAs in the 16-bit GCLA also has at least ve gate delays on the longest path. The GG and GP signals are generated in three gate delays, and the carry signals out of each group are generated in two more gate delays, resulting in a total of ve gate delays to generate the carry out of each group. In the highest bit position (s15), ve gate delays are needed to generate c12, and another ve gate delays are needed to generate s15, for a worst case path of 10 gate delays through the 16-bit GCLA.

With regard to fan-in and fan-out, the maximum fan-in of any gate in a four-bit CLA is four (refer to Figure 3-17), and in general, the maximum fan-in of any gate in an n-bit CLA is n. Thus, the maximum fan-in of any gate in a 16-bit CLA is 16. In comparison, the maximum fan-in for a 16-bit GCLA is ve (for generating c16).

The fan-outs for both cases are the same as the fan-ins. In summary, the 16-bit CLA has only half of the depth of the 16-bit GCLA ( ve gate delays vs. 10 gate delays).

The highest fan-in for a 16-bit CLA is 16, which is more than three times the highest fan-in for a 16-bit GCLA (16 vs. ve). The highest fan-outs are the same as the highest fan-ins for each case.

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