Bit-Sequential Arithmetic for Parallel Processors

A bit-sequential processing element with O(n) complexity is described, where n is the wordlength of the operands. The operations performed by the element are A * B + C * D, A/B, and √A. The operands are fixed point or floating point numbers with variable precision. The concept of semi-on-line algorithms is introduced. A processing element that uses semi-on-line algorithms produces a result δ clock cycles after the absorption of the n-bit operands, where δ is small compared to n. In the paper the processing element and the algorithms are described. A performance comparison between the bit-sequential processing element and conventional pipelined arithmetic units is given.