FPGA-specific decimal sign-magnitude addition and subtraction

ABSTRACT

The interest in sign-magnitude (SM) representation in decimal numbers lies in the IEEE 754-2008 standard, where the significand in floating-point numbers is coded as SM. However, software implementations do not meet performance constraints in some applications and more development is required in programmable logic, a key technology for hardware acceleration. Thus, in this work, two strategies for SM decimal adder/subtractors are studied and six new Field Programmable Gate Array (FPGA)-specific circuits are derived from these strategies. The first strategy is based on ten’s complement (C10) adder/subtractors and the second one is based on parallel computation of an unsigned adder and an unsigned subtractor. Four of these alternative circuits are useful for at least one area-time-trade-off and specific operand size. For example, the fastest SM adder/subtractor for operand sizes of 7 and 16 decimal digits is based on the second proposed strategy with delays of 3.43 and 4.33 ns, respectively, but the fastest circuit for 34-digit operands is one of the three specific implementations based on C10 adder/subtractors with a delay of 4.65 ns.

KEYWORDS:

• Carry-chain
• decimal arithmetic
• IEEE 754-2008
• programmable logic
• sign-magnitude

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the Agencia Nacional de Promoción Científica y Tecnológica, Argentina, through Project PICT 2009–0041.