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Computer Hardware User's Guide

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Floating-Point Multiplication
5-28
Figure 5–16. Flowchart for Floating-Point Multiplication
α(
man
)
b
(
man
) α(
exp
)
b
(
exp
)
(1) (2)
Multiply mantissas Add exponents
c
(
man
) = α(
man
) x
b
(
man
)
(50-bit result)
c
(
exp
) = α(
exp
) +
b
(
exp
)
Put
c
(
man
) in extended pre-
cision floating-point format
Test for special cases of
c
(
man
)
c
(
man
) > > 1
and
c
(
exp
) =
c
(
exp
) + 1
c
(
man
) > > 2
and
c
(
exp
) =
c
(
exp
) + 2
c
(
exp
) =–128
(4)
Right shift 1
to normalize
(5)
Right shift 2
to normalize
(3)
c
(
man
) = 0
(6)
No shift
to normalize
Dispose of extra bits
Test for special cases of
c
(
exp
)
(12)
c
(
exp
) underflow
(13)
c
(
exp
) in range
(11)
c
(
exp
) overflow
If
c
(
man
) > 0,
set
c
(
exp
) to most
positive value
If
c
(
man
) < 0,
set
c
(
exp
) to most
negative value
c
(
exp
) = –128
c
(
man
) = 0
Set
c
to final result
c
= α x
b
(14)
(15)
(16)
(10)
(9)(8)(7)