# CP15_eps - 1 1 Machine precision and errors 2 Machine...

This preview shows pages 1–2. 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: 1 1 Machine precision and errors 2 Machine representation and precision Every computer has a limit how small or large a number can be A computer represent numbers in the binary form. Word length: number of bytes used to store a number Most common architecture: Word length = 4 bytes = 32 bites Word length = 8 bytes = 64 bites ( 1 byte = 1 B = 8 bits: 00000000 ) 3 Integer numbers For a 8 bit computer The highest number then: 2 8 – 1 (–1 because the first is “0”) Since we need 1 bit for +/- Then the highest number is 2 7 – 1 = 127 For 32-bit computers all integer numbers are in the range 2 31 – 1 = 2,147,483,647 1 2 3 4 5 6 7 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 4 Floating point numbers------------------------ Three blocks ----------------------------- 0 1000 0000 1000000 0000 0000 0000 0000 signbit 8-bit exponent 23-bit mantissa range of exponent [-127,128] Single precision : 6-7 decimal places Double precision : 15-16 decimal places 127 exp 2 ) 1 ( − ⋅ ⋅ − = mantissa x S float 7 23 10 2 . 1 2 1 − ⋅ ≈ 15...
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

CP15_eps - 1 1 Machine precision and errors 2 Machine...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online