Overflow Detection and Correction in a Fixed-Point Multiplier

Abstract

The fixed-point binary representation, an integer Correction (ODAC) in order to produce useful results under format with an implied binary point, is an alternative to the overflow conditions. Because multiplication among fixed-IEEE floating-point binary layout. Systems that do not support point numbers is more prone to overflow than other basic the IEEE floating-point format, e.g., mobile devices, use the arithmetic operations, this paper describes a fixed-point fixed-point format because it fits well into integer data paths multiplier using ODAC.whereas floating-point requires its own data path. Software Mult usingtoDAC.developers who port to fixed-point systems often face issues when Mostcapplicatins r ntfixed-pointn s usin balancing range and precision. Those issues, overflow and large 2's-complement integers and define the binary point's position rounding errors, often arise from arithmetic operations, making prior to runtime. The position of the binary point determines debugging more difficult. The proposed solution limits hardware the power of two of each bit; the bits before the binary point support to a set of fixed-point formats and adjusts the format of are positive powers of two starting from zero while the bits the output based on the user supplied format and overflow. The after the binary point are negative powers of two starting from format of the result is readjusted on overflow in order to return a negative one. To help describe the binary point position of a useful result but with the sacrifice of precision. In addition to the fixed-point integer, the Q-notation, QIF, states that a binary corrected result, the overflow flag is raised so the software and subsequent logic are aware of the readjustment in the result's number contains I integer bits and F fractional bits, which may format. This work has been implemented in a fixed-point not add up to the total number of bits in the number. In this multiplier because multiplication yields the largest overflow paper, the Q-notation counts all the bits, including the sign bit, among the four basic arithmetic operations. In order to detect so that the sum of I and F equals the bit-width of the binary overflow early, the fixed-point multiplier adopts preliminary number. overflow detection. With the idea of taking the burden of fixedMultiplying two operands of the same integer format point scaling off of the programmer, the fixed-point multiplier naturally yields a result that is double the bit-width than the with overflow detection and correction provides a starting point operands. The same is true for fixed-point numbers; if the towards mitigating fixed-point errors.operands are both QIF, the product will be Q(21).(2F). In the case of mixed-format multiplication where one operand is