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This e-book offers the methodologies and for embedded platforms layout, utilizing box programmable gate array (FPGA) units, for the main glossy purposes. assurance contains state of the art examine from academia and on a variety of subject matters, together with functions, complicated digital layout automation (EDA), novel method architectures, embedded processors, mathematics, and dynamic reconfiguration.

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The outputs of both dividers are the reciprocal of the divisor and the quotient. The outputs of the NR iterations and of the last multiplier used to calculate 1x × z are numbers represented in radix-1000. Therefore, a final radix-1000 to decimal conversion is used to obtain the reciprocal and the final division result in binarycoded decimal (BCD). A radix-1000 number, r, is represented with radix-1000 digits, r = rn rn−1 . . r1 r0 , where each ri digit is a decimal number from 0 to 999. Therefore a radix-1000 number has the following decimal value: r = rn × 103×n + rn−1 × 103×(n−1) + .

I) If the error ENR (theoretical error without truncation) at iteration i is given by (i) ENR = 1 − y(i) x (i) then the error ENR at iteration i + 1 is given by (i+1) ENR (i) = x (ENR )2 (6) [15]. As, for each piecewise approximation, x is a number in the interval [X0, X1[ then x < X1, and the NR iteration errors (in this case, the first two iterations) are upperbounded by (1) ENR < X1 (E p1 )2 (2) ENR < X12 (E p1 )4 . 1, 1[ is divided into subintervals of size 10−1. As shown, the use of subintervals of size 10−3 is sufficient to provide an error lower than 10−8 after one NR iteration, and an error lower than 10−18 after two NR iterations.

P. C. Neto Fig. 3 Binary to Radix-1000 Converter The binary to radix-1000 converter (BIN2B1000 block in Fig. 3) is based on the architecture proposed in [13] to convert a 20-bit binary number to a two-digit radix-1000 number. The BIN2B1000 converter used in the minimax polynomial calculation only needs to convert a 14-bit binary number (see Fig. 5). The circuit converts a binary number b ∈ [0, 9999] to one decimal digit plus a digit base-1000 number r, that is b = r1 · 103 + r0 = r. Considering that b = b1 · 210 + b0 it follows that b = b1 · 1024 + b0 = b1 · 1000 + b1 · 24 + b0 b1 ≤ 10 = 9999 1024 b0 ≤ 1023, (17) c where c = b1 · 24 + b0 c ≤ 1215 ← 11 bits.

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