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Material Type: Notes; Class: Computer Arithmetic; Subject: Electrical & Computer Enginrg; University: George Mason University; Term: Unknown 1989;
Typology: Study notes
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Unsigned Integer Division Overflow
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Sequential Integer Division Basic Equations
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Fig. 13.2 Examples of sequential division with integer and fractional operands.
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Unsigned Fractional Division Overflow
zfrac < dfrac
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Sequential Fractional Division Basic Equations
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Sequential Fractional Division Justification
s(1)^ = 2 zfrac - q-1 dfrac s(2)^ = 2(2 zfrac - q-1 dfrac) - q-2 dfrac s(3)^ = 2(2(2 zfrac - q-1 dfrac) - q-2 dfrac) - q-3 dfrac
s(k)^ = 2(... 2(2(2 zfrac - q-1 dfrac) - q-2 dfrac) - q-3 dfrac...
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Restoring Unsigned Integer Division
s(0)^ = z
for j = 1 to k
if 2 s(j-1)^ - 2k^ d > 0 qk-j = 1 s(j)^ = 2 s(j-1)^ - qk-j (2k^ d) else qk-j = 0 s(j)^ = 2 s(j-1)
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Fig. 13.5 Shift/subtract sequential restoring divider.
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Fig. 13.6 Example of restoring unsigned division.
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Fig. 13.7 Example of nonrestoring unsigned division.
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Fig. 13.8 Partial remainder variations for restoring and nonrestoring division.
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Fig. 13.10 Shift-subtract sequential nonrestoring divider.
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Non-Restoring Signed Integer Division
s(0)^ = z for j = 1 to k if sign(s(j-1)) == sign(d) qk-j = 1 s(j)^ = 2 s(j-1)^ - 2k^ d = 2 s(j-1)^ - qk-j (2k^ d) else qk-j = - s(j)^ = 2 s(j-1)^ + 2k^ d = 2 s(j-1)^ - qk-j (2k^ d) Correction_step q = BSD_2’s_comp_conversion(q);
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Fig. 13.9 Example of nonrestoring signed division.
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Non-Restoring Signed Integer Division
z = q d + s
z = (q-1) d + (s+d) z = q’ d + s’
z = (q+1) d + (s-d) z = q” d + s”
