Decimal Arithmetic FAQ (Frequently Asked Questions)

Most computers today support binary floating-point in hardware. While suitable for some purposes, such as mathematical analysis, this form of arithmetic is unsuitable for financial, commercial, and human-centric (such as Web) applications. These pages explain why this is so, and also attempt to answer some common questions about decimal floating-point arithmetic.

Please send any comments, new questions, and corrections directly to me (Mike Cowlishaw, mfc@speleotrove.com).
For information on decimal implementations, standards, and other links, please see the General Decimal Arithmetic page.

Contents

1. General
   • Why the increasing emphasis on decimal arithmetic?
   • What problems are caused by using binary floating-point?
   • Do applications actually use decimal data?
   • Why are trailing fractional zeros important?
   • How much precision and range is needed for decimal arithmetic?
   • What rounding modes are needed for decimal arithmetic?
   • Which programming languages support decimal arithmetic?
   • What disadvantages are there in using decimal arithmetic?

2. Definitions
   • What does Algorism mean?
   • What does precision mean?
   • What is the difference between a minus and an en dash?
   • What are Normal numbers, Subnormal numbers, E_max, etc.?

3. Decimal Arithmetic and Hardware
   • Why doesn’t hardware support decimal arithmetic directly?
   • Why did computers use binary in the first place?
   • Surely software emulation of decimal arithmetic is fast enough?
   • Do ‘hand-held’ calculators use decimal arithmetic?
   • Has any company formally announced hardware decimal floating-point support?

4. Decimal Arithmetic Specification
   • Why is decimal arithmetic unnormalized?
   • What are the advantages of normalization?
   • How are zeros with exponents handled?
   • Is the decimal arithmetic ‘significance’ arithmetic?
   • Which is larger? 7.5 or 7.500?
   • When (and why) is exponential notation used in strings?

5. Decimal Encodings
   • How are decimal numbers encoded?
   • How is the exponent bias chosen?
   • How are the parts of decimal numbers encoded?
   • How are zeros encoded?
   • Why are the encodings unnormalized?

6. Miscellaneous
   • How many decimal digits are needed to represent a binary floating-point number exactly?
   • How many decimal digits are needed to represent a binary floating-point number reversibly?