University of California, Santa Barbara
The authors introduce implementations of arithmetic operators based on the Binary Stored-Carry-or-Borrow (BSCB) representation. Several BSCB arithmetic elements, including full-adder, ripple-carry adder, and carry look-ahead adder are presented, followed by detailed design of an array multiplier. In the latter design, the conventional initial AND matrix is transformed and expressed with a redundant radix-2 representation. Each line of the resulting matrix is processed by an accumulation operator with the BSCB representation. Due to a specific property of the multiplication process, this operator is simpler than a standard full-adder cell in terms of gate count, while maintaining the same propagation latency.