1 / 15

Background Reading

http://mathforum.org/dr.math/faq/faq.bases.html. Background Reading. Cosc 235 Computer Organization. Number Systems. Objectives. Identify number systems other than decimal Convert between decimal & binary Cite the advantage of the binary number system for machine operation

brendon-mawe
Télécharger la présentation

Background Reading

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. http://mathforum.org/dr.math/faq/faq.bases.html Background Reading

  2. Cosc 235Computer Organization Number Systems

  3. Objectives • Identify number systems other than decimal • Convert between decimal & binary • Cite the advantage of the binary number system for machine operation • Cite the advantages of octal and hexadecimal number systems • Convert between octal and binary • Convert between decimal and BCD

  4. Objectives (con’t) • Convert between binary and hexadecimal • Convert between decimal and hexadecimal • Convert between octal and decimal

  5. General number system • Usually we use X = 10 • Ai can take on values in the range [0, X-1] … Radix point

  6. Binary number system • Many electronic devices have 2 stable states • Problems 110010101112 101000100102 162310 129810

  7. Converting any base to decimal • For base B, the base-10 representation of the number is • E.g.: • 36910 = 3x102 + 6x101 + 9x100 = 300 + 60 + 9 = 36910 • 5618 = 5x82 + 6x81 + 1x80 = 320 +48 + 1 = 36910 • 17116 = 1x162 + 7x161 + 1x160 = 256 + 112 + 1 = 36910 • 1011100012=28+26+25+24+20=256+64+32+16+1=36910

  8. Converting from decimal to binary • Successive divisions by 2 • E.g., 83 • 83 • 41 R 1 • 20 R 1 • 10 R 0 • 5 R 0 • 2 R 1 • 1 R 0 • 0 R 1 => 10100112

  9. Fractional numbers • 0.01112 = 0x2-1 + 1x2-2 + 1x2-3 + 1x2-4 = 0.25 + 0.125 + 0.0625 = 0.437510

  10. Converting decimal fractions to binary • Method for fractional part F: • Repeat until F = 0 or “enough” digits found: • If F >= 0.5: • Bit value = 1 • F = F - 0.5 Else • Bit value = 0 • F = 2 * F

  11. Octal number system • Convenient for dealing with Binary numbers • Typically used on machines where the number of bits per word is a multiple of 3 • Group 3 binary digits together to get one octal digit • 0002 = 08 0012 = 18 • 0102 = 28 0112 = 38 • 1002 = 48 1012 = 58 • 1102 = 68 1112 = 78

  12. Converting from decimal to octal • Successive divisions by 8 • E.g., 830 • 830 • 103 R 6 • 12 R 7 • 1 R 4 • 0 R 1 => 14768

  13. Hexadecimal number system • Convenient for dealing with Binary numbers • Typically used on machines where the number of bits per word is a multiple of 4 • Group 4 binary digits together to get one hex digit 00002 = 016 00012 = 116 00102 = 216 00112 = 316 01002 = 416 01012 = 516 01102 = 616 01112 = 716 10002 = 816 10012 = 916 10102 = A16 10112 = B16 11002 = C16 11012 = D16 11102 = E16 11112 = F16

  14. Converting from decimal to hex • Successive divisions by 16 • E.g., 830 • 830 • 51 R 14 = E • 3 R 3 • 0 R 3 => 33E16

  15. Binary Coded Decimal (BCD) • Represent 0-9 in 4 binary digits • 00002 = 010 • 00012 = 110 • 00102 = 210 • 00112 = 310 • 01002 = 410 • 01012 = 510 • 01102 = 610 • 01112 = 710 • 10002 = 810 • 10012 = 910 • Not binary

More Related