Reviewing High-Radix Signed-Digit Adders

Higher radix values of the form β = 2^r have been employed traditionally for recoding of multipliers, and for determining quotientand root-digits in iterative division and square root algorithms, usually only for quite moderate values of r, like 2 or 3. For fast additions, in particular for the accumulation of many terms, generally redundant representations are employed, most often binary carry-save or borrow-save, but in a number of publications it has been suggested to recode the addends into a higher radix. It is shown that there are no speed advantages in doing so if the radix is a power of 2, on the contrary, there are significant savings in using standard 4-to-2 adders, even saving half of the operations in multi-operand addition.