Impact of Radix-10 Redundant Digit Set [−6, 9] on Basic Decimal Arithmetic Operations

Abstract

Redundant-digit decimal computer arithmetic, with the principal property of carry-free addition, has been the subject of several studies, as the relevant literature contains a wide variety of decimal digit sets and their binary representations. For example, symmetric decimal signed digit sets [-α, α], for α ∈ {5,6,7,8,9 }, and the asymmetric ones, such as [-8,9], [ -9,7], and [ 0,15 ], have been the basis of variant hardware architectures for decimal arithmetic operations. However, digit sets with the minimal 4-bit representations show better figures of merit. In this work, we present a new decimal digit set [-6,9], called diminished-6 overloaded decimal digit set (DODDS). Its special 4-bit representation contains two posibits (weighted 2³ and 2⁰) and two negabits (weighted 2² and 2¹). Design and implementation of the corresponding carry-free decimal adders and subtractors are thoroughly discussed. Furthermore, to cover the requirements of all possible DODDS applications in decimal multipliers, dividers, and square rooters, we provide adder/subtractor designs for a variety of input combinations of DODDS and binary coded decimal (BCD) operands, all with DODDS output (e.g., DODDS + BCD = DODDS, which is useful in BCD partial product reduction). Analytical and synthesis-based evaluations and comparisons with similar previous works show the notable merits of DODDS over the other redundant decimal digit sets.