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INDEX
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Newton Raphson, 109, 155, 180, 208, 439, 444, 477 convergence graph, 156 Nonrecurring engineering cost (NRE), 242, 252 Normalization additive, 468 circuit, 530 exponential additive, 188, 191 oating point numbers, 515, 523 multiplicative, 467 NRE, see Nonrecurring engineering cost Number integer, 15, 42 natural, 15, 39 representation, 1, 6 Number representation system(s), 39 positional, 40 weighted, 39 Number theory, 15 Numeration system base-B, 40 binary, 40 decimal, 40 xed-point, 51 hexadecimal, 40 mixed-radix, 22, 40 octal, 40 Order of an element, 25, 26 Over ow detection, 74 oating-point, 524 Parallel (3,2)-counter, 337 Parallel counter, 379 Partial remainder divisor plot diagram, see P-D diagram Partitioning hardware software, 3, 8 P-D diagram, 139, 140 Pentium bug, 148 Per Gelosia, 98, 383, 401
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INDEX
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nonredundant, 148 redundant, 149 Range of positive numbers, 52 of represented numbers, 52 relative, 53 Rate, sample, 281 Reciprocal computation, 157 Reduced instruction set computer (RISC), 245, 248 Redundant base-B coding, 166 set of digits, 50 systems, 166 Remainder, 16, 28, 110 carry-stored representation, 132 Req signal, 284 Residue number system (RNS), 39, 42, 173, 455, 458 to mixed-radix, 458 representation, 42 Residues modulo mi, 173 Resource computation, 272 connection, 272 memory, 272 Ring, 27 commutative, 32 nite, 211 polynomial, 27, 211 Ripple-carry adder, 289, 360 array, 366, 372 B-ary adder, 384 multioperand adders, 378 multiplier, 360, 365 RISC, see Reduced instruction set computer RNS, see Residue number system Robertson diagram, 119, 139 Rounding circuit, 530 oating-point numbers, 515 schemes, 524 Sample rate, 281 Scheduling, 277 SDFA, see Signed-digit, full adder Self-timed adder, 285 circuit, 282 pipelined circuit, 284 Self-timing, 282 Semigroup, 26
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f(n), 24 PicoBlaze, 8, 9, 12 Pipeline, 281, 283 latchless technique, 282 (p,k)-counter, 378 PLD, see Programmable logic device Polynomial, 27 approximation, 180, 183 computation, 463 constant, 27 irreducible, 28 monic, 28 multiplication, 227 zero, 27 0-degree, 33 Power consumption, 242, 245 Precedence graph, 277 relation, 277 scheduled, 278 Precision absolute, 51 relative, 51 Pre x carry chain, 318 Prescaling, 185 Prime, 16 relatively, 16, 24 Primitive element, 25 Private key, 5 Processor, 245. See also Application speci c instruction set processors; Complex instruction set computers; Digital signal processor; Reduced instruction set computer; Very long instruction word embedded, 248, 250 general-purpose (GPP), 246 harvard architecture, 246 microcontroller, 2, 248 microprocessor, 2, 247 programming instruction-set, 251 superscalar, 247 von Neumann architecture, 246 Product, modular, 8 Programmable logic, 256. See also Field programmable gate array Programmable logic device (PLD), 256 Propagate function, 56, 292 generalized, 58, 301 Prototype, 12 Prototyping board, 8
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Q-select, 143 Quotient, 16, 28, 110 Quotient-digit
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Sign bit extension, 46 Signed systems, 166 Signed-digit, 166 counter, 402 full adder, 402 multiplier, 397 representation, 47 Signi cand, 514 Sign-magnitude, 166 adder, 355 addition, 79 representation, 42 subtraction, 79 subtractor, 355 Sine and cosine, 470 CORDIC algorithm, 471 SOC, see System-on-chip Spartan, 8, 260 263 Square root, 104 base-2, 106 base-B, 104 cellular carry-save, 104 oating-point, 522, 546 Square rooter, 472 Newton Raphson, 477 nn-restoring shift-and-subtract, 475 restoring shift-and-subtract, 472 Square rooting, 165, 198 convergence method, 208 digit recurrence, 198 integer in base-B, 200 Newton-Raphson, 208 nonrestoring binary add-and-subtract, 204 restoring binary shift-and-subtract, 202 Standard cell, 2 Start signal, 284 Stat-done ag, 347, 349 Statistical approach, 348 Sticky bit, 527 Stored-carry encoder, 68, 333 (5,2)-, 342 (5,2)-, 341 (7,3)-, 338, 340 (p,k)-, 338 form, 68, 69 Sub eld, 33 Subtraction, 55 B s complement, 74 excess-E, 78 oating-point numbers, 518 modulo m, 213 natural numbers, 71, 344 sign magnitude, 79
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INDEX Subtractor, 289, 344 B s complement, 350 excess-E, 352 oating-point, 527 modulo m, 481 ripple-carry, 344 sign-magnitude, 355 Synthesis, 3, 10, 14, 271 System-on-chip (SOC), 2. See also Embedded systems Taylor expansion, 35 Taylor series, 35 Taylor-MacLaurin, 165, 180, 183 expansions, 109, 155 series, 181 Termination detection, 346 FPGA implementation, 348 Throughput, 271, 283 average, 284 Time-to-market, 243 Tree carry-save, 339, 342, 343 multioperand addition, 332 Wallace/Dadda, 378 Trigonometric, 165, 182, 193, 463 functions, 180 Truncation, oating-point numbers, 524 Ulp, see Unit in the least signi cant position Under ow, oating-point, 524 Unit in the least signi cant position (ulp), 51, 52, 109 Verilog, 267 Very long instruction word (VLIW), 246 VHDL, 267 Virtex, 260 265 VLIW, see Very long instruction word Wallace/Dadda tree, 378 Zn, 24 Zp inversion, 223 operations, 222 Zp [x]/f (x) adder, 500 addition, 224 multiplication, 225 operations, 224, 500 subtraction, 224 subtractor, 500
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