A decimal fully parallel and pipelined floating point multiplier

Decimal Floating Point Number System

“…We will focus our attention here on designs using the conventional paradigm of CMOS digital gates although some alternative technologies [8,9] were also considered for decimal circuits at different points in time. Commercial hardware designs for decimal floating point additions were pioneered by IBM [10][11][12], followed by SilMinds [6,[13][14][15], then Fujitsu [16]. All of these commercial implementations use DPD.…”

“…DPD designs started first by presenting ideas for carry-save addition for decimal fixed point multipliers [37] then iterative high-frequency multipliers [38] and multioperand addition [39]. That early work combined with partial product generation [40] formed the base for the complete floating point multipliers [41,42] and the innovative ideas [33] relying on the various decimal codes yielding fully parallel floating point multipliers [13,34].…”

“…To maintain the distinction, we should store 0:000000000000050 10 12 First measurement 0:000000000000005 10 13 Second measurement with all those leading zeros. For the standard, both representations are members of the same cohort.…”

Algorithm and architecture for on-line decimal powering computation

“…First, the logarithm results are achieved by accumulating the n-digits rounding values of −log 10 (1 + e j 10 −j ) from the 1 st to the k th iteration. In each iteration, the maximum rounding error of −log 10 (1 + e j 10 −j ) is 0.5 × 10 −n therefore the maximum ε q1 is: Table (LUT) for e j ∈ [− 9,9] followed by a shifter to achieve the multiplication by 10 −j , the maximum rounding error of −ej 10 −j ln (10) is 0.5 × 10 −n therefore the maximum ε q2 is:…”

“…The block diagrams illustrating the architecture of stage 1 and stage 2 are shown in figure(1) and figure(2) respectively. The used Multiplier and CPA are both implemented based on [9] [10]. In the first stage, a multiplier by one digit using Signed Digit (SD) recoding for e j+1 produces two partial products.…”