# Low energy arithmetic/logic gate level design

I'm looking into various gate level (NAND, NOR, AND, INV) designs for low energy arithmetic/logic blocks, especially adders. Low energy indicates the use of minimal energy per operation executed.

Holding $V_{dd}$, technology and clock speed constant, which of the following adder designs are more energy efficient: Ripple, carry lookahead, carry-select, prefix adders? And why is that so?

Independently of full-adder design (which is very important as BarsMonster says), objectively, the most power efficient adder would be the one with the least number of transistors.

Using the same kind of full-adder unit (same quantity of transistors in each FA) in the Adders that you mention, the "smallest" would be the Ripple Carry Adder. All other adders have some sort of extra circuitry to lower the critical propagation delay.

Check out this link: http://users.encs.concordia.ca/~asim/COEN_6501/Lecture_Notes/Lecture_2_Slides.pdf @ pages 40 - 48.

• 9 transistor SRAM uses less power than 6 transistor SRAM. So I suspect that the most power efficient adder is not the one with the least number of transistors. – davidcary Jun 26 '11 at 2:33
• @davidcary You are talking about [SRAM] "Units" there. When it comes to units there are different variants of Full-Adder units and, as I and BarsMonster said, FA design is really important when comparing working and real Adders (as in "at the lab"). That's why I specified that: Independently of full-adder design, the most power efficient architecture of an Arithmetic Adder (here I'm referring to a higher level than FA unit) would be the one with the least number of transistors/FA units. (I guess what confused you was my use of the word "transistors" instead of "FA units"). – Arturo Gurrola Jun 28 '11 at 20:26
• Thank you for the excellent link. My understanding is that a 16-bit carry ripple adder has more full-adder units than a 4-bit carry ripple adder. So I am surprised to learn that, in the experiment you linked to, they both use exactly the same amount of power. – davidcary Aug 31 '11 at 11:50

It's not that simple. There are lots of variants of fulladder itself, with different number of transistors. This is very popular subject, and on IEEE you can easily find many papers with specific benchmark results you are interested in.

I can also add, that going for carry-lookahead added allow you to go for much lower voltage with the same performance level => less total consumption at the same performance level.