Binary-Coded Decimal Arithmetic Instructions

IEEE-754 2008 has extended the standard with decimal floating point arithmetic. Human-centric applications, like financial and commercial, depend on decimal arithmetic since the results must match exactly those obtained by human calculations without being subject to errors caused by decimal to binary conversions. Decimal Multiplication is a fundamental operation utilized in many algorithms and it is referred in the standard IEEE-754 2008. Decimal multiplication has an inherent difficulty associated with the representation of decimal numbers using a binary number system. Both bit and digit carries, as well as invalid results, must be considered in decimal multiplication in order to produce the correct result. This article focuses on algorithms for hardware implementation of decimal multiplication. Both decimal fixed-point and floating-point multiplication are described, including iterative and parallel solutions.

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Decimal Hardware Multiplier

Advanced Methodologies and Technologies in Artificial Intelligence, Computer Simulation, and Human-Computer Interaction - Advances in Computer and Electrical Engineering ◽

10.4018/978-1-5225-7368-5.ch054 ◽

2019 ◽

pp. 722-736

Author(s):

Mário Pereira Vestias

Keyword(s):

Number System ◽

Floating Point ◽

Binary Number ◽

Correct Result ◽

Fundamental Operation ◽

Floating Point Arithmetic ◽

Decimal Arithmetic ◽

Decimal Numbers ◽

Decimal Multiplication ◽

Point Arithmetic

IEEE-754 2008 has extended the standard with decimal floating-point arithmetic. Human-centric applications, like financial and commercial, depend on decimal arithmetic since the results must match exactly those obtained by human calculations without being subject to errors caused by decimal to binary conversions. Decimal multiplication is a fundamental operation utilized in many algorithms, and it is referred in the standard IEEE-754 2008. Decimal multiplication has an inherent difficulty associated with the representation of decimal numbers using a binary number system. Both bit and digit carries, as well as invalid results, must be considered in decimal multiplication in order to produce the correct result. This chapter focuses on algorithms for hardware implementation of decimal multiplication. Both decimal fixed-point and floating-point multiplication are described, including iterative and parallel solutions.

Download Full-text