{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

13-Floating-Point-Number-Systems-4UP

# 13-Floating-Point-Number-Systems-4UP - Floats Examples...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Floats Examples Properties Floating Point Number Systems Dhavide Aruliah UOIT MATH 2070U c D. Aruliah (UOIT) Floating Point Number Systems MATH 2070U 1 / 20 Floats Examples Properties Floating Point Number Systems 1 Floating-point number systems 2 Examples 3 Properties of floating point number systems c D. Aruliah (UOIT) Floating Point Number Systems MATH 2070U 2 / 20 Floats Examples Properties Machine numbers Machine numbers : numbers representable in a computer Conceptually represented in sequence of boxes Example: 6 digit base 10 fixed point number system: . 0 . 0 1 . 0 2 . . . 9 9 9 . 9 9 9 x min = 0.001 = 10- 3 x max = 999.999 ' 10 4 10 6 possible nonnegative machine numbers c D. Aruliah (UOIT) Floating Point Number Systems MATH 2070U 4 / 20 Floats Examples Properties Scientific notation Scientific notation superseded fixed point notation Permits wider range of values with fixed # of symbols Multiply through by powers of 10 to shift decimal to right or left- 1370.1542 =- 0.13701542 × 10 4 ' - 0.137015 × 10 04 0.0000009376 = 0.9376 × 10- 6 Terminology: if x = m × 10 e = ( a 1 a 2 . . . a t ) 10 × 10 e I m = ( a 1 a 2 . . . a t ) 10 = mantissa I e = exponent I a 1 = most significant digit I a t = least significant digit c D. Aruliah (UOIT) Floating Point Number Systems MATH 2070U 5 / 20 Floats Examples Properties Normalised scientific notation Many representations of same number possible, e.g.,- 1370 =- 1370 × 10 =- 137.0 × 10 1 =- 13.70 × 10 2 =- 0.1370 × 10 4 =- 0.001370 × 10 6 =- 13700000 × 10- 4 Normalise : leading nonzero digit to left of decimal point, e.g.,- 1370 =- 0. 1 370 × 10 4 Distinct normalisations possible, e.g.,- 1.370 × 10 3 Same idea works in other bases, e.g., ( 1A5 . 9E ) 16 × 16 = ( . 1A59E ) 16 × 16 3 c D. Aruliah (UOIT) Floating Point Number Systems MATH 2070U 6 / 20 Floats Examples Properties Floating-point number systems Definition (Floating-point number system)...
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

13-Floating-Point-Number-Systems-4UP - Floats Examples...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online