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Engineering Digital Design
book

Engineering Digital Design

by Richard F. Tinder
January 2000
Intermediate to advanced content levelIntermediate to advanced
884 pages
29h 39m
English
Academic Press
Content preview from Engineering Digital Design
2.9 BINARY ARITHMETIC 57
Thus, P
2
= A
2
× (B
2C
) generates the 2’s complement of A
2
× B
2
the form in which a
computer stores the results. The “true” value of P
2
can be obtained by negation, which is
the 2’s complement of the result, that is, P
2
)
2C
= (2
n
A
2
× B
2
)
2C
.
Likewise, if both A
2
and B
2
are negative n-bit operands, then the product (A
2
)×(B
2
)
becomes, after conversion to 2’s complement by Eq. (2.14),
P
2
= A
2C
× (B
2C
)
=(2
n
A
2
) × (2
n
B) Mod 2
n
=2
n
× 2
n
2
n
A
2
2
n
B
2
+ A
2
× B
2
Mod 2
=2
2n
2
n
2
n
+ A
2
× B
2
Mod 2
n
or P
2
= A
2
× B
2
, (2.23)
where 2
2n
2
n
2
n
(Mod 2
n
) = 0. Thus, the product of two negative binary numbers
in 2’s complement notation is the positive product of ...
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Publisher Resources

ISBN: 9780126912951