May 2024
Intermediate to advanced
332 pages
15h 45m
English
Content preview from Discrete Mathematics
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---------------------------SYMBOLIC
LOGIC
85
How about the carry out?
It
turns out that
if
there is a carry out in either the first
or
second half adder,
then we have a carry out for the full adder. Why? The only way we can
get
a carry out is
by
adding 1 +
1.
The
sum
of
three numbers is guaranteed to have two bits (and thus requires a carry out). Now,
if
we have a carry
out
in
one
half
adder, will the other
half
adder also have a carry out? The previous example showed this was
not the case.
Notice that
we
have drawn a large box labelled "Full Adder".
We
can think
of
this as a black box,
inside which are two
half
adders and
an
OR
gate.
Designing ...
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