06-06-2019, 10:10 PM

An extract from Some Recent Developments in the Theory of Significant Figures and their Applications to Chemical Instrumentation, Lawrence D. Fields, Oregon State University, NOV 1985 (106 pgs.)

ABSTRACT

Significant figures have been a nebulous area in the physical sciences. The results of a literature survey, and of a questionaire … revealed widely differing interpretations regarding the proper role of significant figures. The present study has a two-fold nature.

First the existing theory was extended to include the Root Rule, which unambiguously assigns the correct number of significant figures to the result of a chemical or physical calculation. Then significant figure theory was applied in developing improved methods for recording (and transmitting) tables of measurement data. The upshot is two novel data compression techniques - Decimal Coded Binaries (DCB) and Eight Code - which efficiently combine a measurement and its uncertainty into a single number.

…

INTRODUCTION

… two number systems are combined in order to incorporate two types of information - a measurement and its uncertainty - into a single number. The result is a format, which looks and reads like ordinary base 10, and which gives the same information about uncertainty as binary. This type of nomenclature is called Decimal Coded Binaries (DCB)…

…

DCB PROGRAMS FOR THE HP 15C SCIENTIFIC CALCULATOR

Since HP15C programming is rather primitive, there are some limitations, which we must contend with. There are no character variables, nor is there any string manipulation. In particular, the calculator cannot recognize a terminal zero in a decimal fraction; i.e. it cannot distinguish between "1.2" and "1.20". Therefore at times the directions will tell you to ignore decimal points, to pretend that real numbers are integers. At other times, the instructions will tell you how to use your common sense in order to put the decimal point in its proper place. Since the simplest concepts are often the most difficult to explain, the directions may seem more complicated than they really are…

Program for Expressing Measurement Data in a DCB Format

This first program transforms experimental data into DCB notation…

HP15C Program for Decoding DCB.

This second program translates DCB into plain English…

Fully Documented.

BEST!

SlideRule

ABSTRACT

Significant figures have been a nebulous area in the physical sciences. The results of a literature survey, and of a questionaire … revealed widely differing interpretations regarding the proper role of significant figures. The present study has a two-fold nature.

First the existing theory was extended to include the Root Rule, which unambiguously assigns the correct number of significant figures to the result of a chemical or physical calculation. Then significant figure theory was applied in developing improved methods for recording (and transmitting) tables of measurement data. The upshot is two novel data compression techniques - Decimal Coded Binaries (DCB) and Eight Code - which efficiently combine a measurement and its uncertainty into a single number.

…

INTRODUCTION

… two number systems are combined in order to incorporate two types of information - a measurement and its uncertainty - into a single number. The result is a format, which looks and reads like ordinary base 10, and which gives the same information about uncertainty as binary. This type of nomenclature is called Decimal Coded Binaries (DCB)…

…

DCB PROGRAMS FOR THE HP 15C SCIENTIFIC CALCULATOR

Since HP15C programming is rather primitive, there are some limitations, which we must contend with. There are no character variables, nor is there any string manipulation. In particular, the calculator cannot recognize a terminal zero in a decimal fraction; i.e. it cannot distinguish between "1.2" and "1.20". Therefore at times the directions will tell you to ignore decimal points, to pretend that real numbers are integers. At other times, the instructions will tell you how to use your common sense in order to put the decimal point in its proper place. Since the simplest concepts are often the most difficult to explain, the directions may seem more complicated than they really are…

Program for Expressing Measurement Data in a DCB Format

This first program transforms experimental data into DCB notation…

HP15C Program for Decoding DCB.

This second program translates DCB into plain English…

Fully Documented.

BEST!

SlideRule