This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Lecture 5 Today’s class: • Representations of numbers in different bases • Floatingpoint numbers & machine representations • Arithmetic with floatingpoint numbers Material on floatingpoint numbers, machine arithmetic, and rounding errors introduces many extremely technical subtleties. Unfortunately, it is often required (even for non computer scientists) to understand these technicalities as consumers of numerical software! • Taylor’s theorem and truncation errors (next time) Representations of numbers XLIII × XXXVII MDXCI 43 × 37 301 1290 1591 Decimal representations • Recall: 71 . 32 actually means 7 1 . 3 2 = 7 · 10 + 1 · 1 + 3 10 + 2 100 = 7 · 10 1 + 1 · 10 + 3 · 10 1 + 2 · 10 2 7 tens + 1 unit + 3 tenths + 2 one hundredths integer part = 71 , fractional part = 0 . 32 • Positional notation needs digit zero & decimal point • Decimal system favoured by most modern humans Floatingpoint format • Floatingpoint format : scientific notation • Normalised: shift decimal point ( × powers of 10) 1 . 3701542 · 10 3 = 1370 . 1542 9 . 376 · 10 7 = 0 . 0000009376 • Terminology: if x = s · 10 e = ( a .a 1 a 2 ...a t ) 10 · 10 e – s = ( a .a 1 a 2 ...a t ) 10 = significand – f = (0 .a 1 a 2 ...a t ) 10 = mantissa (fraction) – t = precision = # digits in mantissa – e = exponent of base b = 10 Different number systems • Different civilisations used different numeral bases • Number systems distinguished by...
View
Full
Document
This note was uploaded on 06/20/2011 for the course MATH 2070 taught by Professor Aruliahdhavidhe during the Winter '10 term at UOIT.
 Winter '10
 aruliahdhavidhe

Click to edit the document details