# Ch 5 - Chapter 5 Unavoidable Errors in Computing z Program...

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Chapter 5 – Unavoidable Errors in Computing ± Program “bug” is avoidable, but occur often ± An error in software ± Fixing the error is called “debugging” ± Some errors in mathematical computing are unavoidable ± Roundoff Errror - digits to the right of decimal are discarded ± Truncation Error - approximate a continuous function with discrete values Example: ± Roundoff Errror: 1000+0.00000000001 = 1000 ± Truncation Error: 10000 11 ii ! "" # \$\$ 1 Digital Representation of Numbers ± Fixed number of digits represent a number ± Less memory and more speed ± But causes roundoff error ± Bits, Bytes, and Words ± bit is a binary digit (0 or 1) ± byte is a group of eight bits ± word is smallest addressable unit of memory for a particular computer ± Types of Numbers ± Integers 3, 786, -29 ± Real Numbers 1.67, 1.0e-7, 9.7e13 ± Complex Numbers 1+i, 2+7i 2

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Representation of Numbers - Integers ± Represented by fixed number of binary digits ± Base 2 system 25 = 16 + 8 + 1 = 2 4 + 2 3 + 2 0 = (11001) 2 (11111) 2 = 2 4 + 2 3 + 2 2 + 2 1 + 2 0 = 31 ±
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## This note was uploaded on 01/29/2011 for the course PGE 310 taught by Professor Klaus during the Spring '06 term at University of Texas.

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Ch 5 - Chapter 5 Unavoidable Errors in Computing z Program...

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