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Computer Hardware User's Guide

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Floating-Point Addition and Subtraction
5-33
Data Formats and Floating-Point Operation
Figure 5–17. Flowchart for Floating-Point Addition
α(
man
)
b
(
man
) α(
exp
)
b
(
exp
)
(3)
(2)
Align mantissas
Subtract exponents
α(
man
) = α(
man
) > >
d
Discard LSBs to keep
α(
man
) in extended-
precision floating-
point format
d
=
b
(
exp
) ± α(
exp
)
c
(
man
) =
c
(
man
) > > 1
c
(
exp
) =
c
(
exp
) + 1
Discard LSBs to keep in
extended-precision
floating-point format
Test for special cases of
c
(
man
)
c
(
exp
) = –128
(6)
Overflow of
c
(
man
)
(7)
k = # of leading
non-significant
sign bits
(5)
c
(
man
) = 0
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
to most
positive value
If
c
(
man
) < 0,
set
c
to most
negative value
set
c
to 0
c
(
exp
) = –128
c
(
man
) = 0
Set
c
to final result
c
= α +
b
(14)
(15)
(16)
(8)
(1)
Compare exponents
If α(
exp
) < =
b
(
exp
)
c
(
exp
)=
b
(
exp
)
else
c
(
exp
)= α(
exp
)
(Assume for simplicity
that α(
exp
) < =
b
(
exp
))
(4)
Add mantissas
c
(
man
) = α(
man
) +
b
(
man
)
c
(
man
) < < k
c
(
exp
) =
c
(
exp
) –k
(10)
(9)