2: Numbers and Errors

97-09-17


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Table of Contents

2: Numbers and Errors

Computer representation of numbers

Number systems (Decimal)

Number Systems (Binary)

Converting numbers from one base to another

Converting from one base to another (conít)

Converting from one base to another (conít)

Other common bases

Floating point representation of numbers

IEEE 754 Floating point storage

IEEE 754 Floating point storage (contíd)

IEEE 754 Floating point conít

Characteristics of floating point numbers

Characteristics of floating point numbers

Characteristics of floating point numbers (conít)

Characteristics of floating point numbers (contíd)

Characteristics of floating point numbers (contíd)

Characteristics of floating point numbers (contíd)

Intermediate calculations

Error Definitions

Significant Digits

Significant digits and the machine unit

Significant digits example

Significant digits and rounding

Sources of Error

Sources of errors

Sources of errors

Machine errors: Loss of significant digits when doing a calculation

Machine errors (continued)

Machine errors (continued)

Machine errors (continued)

Machine errors (continued)

Machine errors (continued)

Machine Errors (Conít)

Mathematical Approximation Errors

Mathematical Approximation Errors

Error Propagation

Error Propagation (conít)

Propagation of error (conít)

Propagation of error (conít)

Propagation of error (conít)

Propagation of errors in summations

Propagation of error in summations (conít)

Author: J. Rolia

Email: nholtz@ccs.carleton.ca

Home Page: http://civeng.carleton.ca/94.266/slides/numbers