Arithmetic operators based on the binary stored-carry-or-borrow representation

We 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-lookahead 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. The entire multiplier is implemented with only XOR and AND gates, thus improving its testability and reliability.