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Contest
Entry # DL205: Better Adders for the AT40K FPGAs
Abstract.
Adder speed and size are undeniably crucial factors in determining
the success of a family of FPGAs. I will present fast, small
adders for the AT40K FPGA family.
These
adders are simple carry-skip adders specifically designed for
FPGAs, where cells and interconnects are optimized for ripple
chains. Our adders make good use of these optimized ripple chains
instead of trying to outperform them. Yet I composed ripple
chains in such a way that shortens the critical path delay significantly
without too much cost.
As
an example I have completely designed a 16-bit adder and a 32-bit
adder. Our 16-bit adder is approximately 23.5% faster than its
ripple counterpart, and is 37% larger. The 32-bit adder,
on the other hand, is 34% faster than its ripple counterpart,
while using only 28% more cells. On the contrary, a 16-bit
carry-select adder automatically generated by Atmel's IDS is
more than 3 times as large as the ripple adder, and sometimes
operates more slowly than ripple adders in practice.
Unlike
the IDS’s carry-select adders, our carry-skip adders don’t duplicate
ripple chains for any bit position. Instead, our adders divide
the adder’s bit positions into groups, and determines inexpensively
whether the carry into a group will be propagated through to
as carry out of that group. If so, that group is said to be
"skipped." The carry out of a skipped group of bits
can be determined with a multiplexer without having to wait
for the carry in to ripple slowly through the bit positions
of that group.
(Click to Enlarge)
In
our 16-bit adder, the 16 bit positions are divided into 3 blocks
of sizes 5, 6, and 5. Our 32-bit adder is divided up into blocks
of sizes 10, 12, and 10. In both adders, the most and least
significant blocks are just ordinary ripple adder blocks, but
the middle block is a special block with a skip mechanism. No
carry signal ripples slowly all the way through from lsb to
msb, making the worst-case delay much better than that of the
ripple adder.
End
of Abstract
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