11FastDividersLecture 102Classification of DividersSequentialRadix-2 High-radixRestoringNon-restoring• regular• SRT• using carry save adders• SRT using carry save addersArrayDividersDividersby Convergence3Fig. 15.7 Restoring array divider composed of controlledsubtractor cells.24Restoring Unsigned Fractional Divisions(0)= zfor j = 1 to kif 2 s(j-1)- d > 0q-j= 1s(j)= 2 s(j-1)- q-jdelseq-j= 0s(j)= 2 s(j-1)5Fig. 15.8 Nonrestoring array divider built of controlledadd/subtract cells.6Non-Restoring Unsigned Fractional Divisions(0)= zq1= 1for j = 0 to kif q-(j-1) = 1s(j)= 2 s(j-1)- delses(j)= 2 s(j-1)+ dif s(j) > 0q-j= 1elseq-j= -1if s(k)< 0s(k) = s(k) + dq = q - 137Fig. 14.3 The new partial remainder, s(j), as a function of the shifted old partial remainder, 2s(j–1), in radix-2 nonrestoring division.8Fig. 14.4 The new partial remainder s(j) as a function of 2s(j–1), with q–j in {–1, 0, 1}.9Fig. 14.5 The relationship between new and old partial remainders in radix-2 SRT division.410SRT Unsigned Fractional Divisions(0)= zfor j = 1 to k if s(j-1) ≥ 1/2q-j= 1s(j)= 2 s(j-1)- delseif s(j-1)< -1/2q-j= -1s(j)= 2 s(j-1)+ delseq-j= -1s(j)= 2 s(j-1)if s(k)< 0s(k) = s(k) + dq = q - 11112513Fig. 14.6 Example of unsigned radix-2 SRT division.14Fig. 14.8 Block diagram of a radix-2 divider with partialremainder in stored-carry form.15Using Carry-Save Adders with the Dividerssum = u = u1u0.u-1u-2u-3u-4….u-kcarry = v = v1v0.v-1v-2v-3v-4….v-kt = u1u0.u-1u-2+ v1v0.v-1v-2u + v - t = 00.00u-3u-4….u-k +00.00v-3v-4….v-k< 0 ≤12616Using Carry-Save Adders with the Dividers0t12-t ≥ 0q-j= 1t <q-j= -112-≤ u+v <12-12≤ t < 012-q-j= 0u+v < 0u+v ≥ 01718Fig. 14.7 Constant thresholds used for quotient digitselection in radix-2 division with qk–j in {–1, 0, 1}.719Fig. 14.10 A p-d plot for radix-2 division with d ∈ [1/2,1), partial remainder in [–d, d), and quotient digits in [–1, 1].20Radix-4 division in dot notation21Fig. 14.11 New versus shifted old partial remainder in radix-4 division with q–j in [–3, 3].822Fig. 14.12 p-d plot for radix-4 SRT division with quotient digit set [–3, 3].23Radix-4 SRT divider with the digit set {-2, -1, 0, 1, 2}2492526Fig. 15.9 Sequential radix-2 multiply/divide
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