A library of on-line arithmetic structures is presented. Their ability to p
roduce and consume the most significant digit first allows subsequent compu
tations to begin earlier, shortens the execution time of variable precision
and composite operations, and simplifies interconnection networks which ca
n help preserve high clock rates in large digit-serial designs. More import
antly, designers can interconnect individual units without designing interm
ediate structures to reformat data, a luxury that is currently unavailable
to FPGA designers wishing to use bit-serial arithmetic. The on-line structu
res introduced are small, and can be easily combined to yield more powerful
blocks. The library's applicability to signal processing applications is d
emonstrated with the DFT, DCT and FIR filter. Results indicate high area ef
ficiency and rapid execution speed.