2.1 From the Class Notes link on the Course Home PageIndex

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• 010_arithmetic_terms.txt - Basic Arithmetic Operations and Terminology - precedence, exponents, prefixes, bases, fractions, scientific notation
• 020_operation_output_size.txt - Size needed for output of ADD and MULTIPLY
• 030_binary_math.txt - Binary Integer Mathematics, unsigned, two’s complement, etc.
• 050_hexadecimal_conversions.txt - Converting to/from hexadecimal (base 16)
• 060_different_binary_integers.html - Representation for 4-bit Signed Integers in Different Systems
• 070_integer_encoding_practice.html - Integer Encoding Practice
• 080_byte_order_endian.html - Byte Order - Big and Little Endian

2.2 From Blackboard Course DocumentsIndex

These documents have restricted distribution and cannot be put on the Course Home Page.

• 01.ppt - Introduction (vonNeumann, prefixes, reciprocal)
• 02.ppt - Data Representation
  • omit “Booth’s algorithm” slides 50-52
  • ignore slides 63-70 (the “simplified” model)
  • slide 72 is wrong: IEEE 754 +0.0 is equal to -0.0
  • ignore slides 75-76 (floating-point multiplication)
    • use my web pages and assignments instead for floating-point info
  • you do not need to know how to do math with sign-magnitude numbers
    • you do need to know how to convert them to/from decimal
  • you do not need to know how to do math with one’s complement numbers
    • you do need to know how to convert them to/from decimal
  • you need to know how to do addition with two’s complement numbers
    • you also need to know how to convert them to/from decimal
  • you do not have to multiply or divide or subtract any binary numbers
  • omit most of the math in 2.8 “Error Detection and Correction”
  • omit slides 94-100
  • omit slides 103-115
• 05.ppt - instruction set architectures
  • only read endian-ness on slide 7
  • omit the rest of this slide set

2.3 From the InternetIndex

• http://en.wikipedia.org/wiki/Category:Computer_arithmetic

• http://en.wikipedia.org/wiki/Computer_numbering_formats

• http://en.wikipedia.org/wiki/Binary_numeral_system

• http://en.wikipedia.org/wiki/Octal

• http://en.wikipedia.org/wiki/Hexadecimal

• http://www.cs.nmsu.edu/~pfeiffer/hc11/notes/binary.html

• http://www.exploringbinary.com/the-answer-is-one-unless-you-use-floating-point/

• “odometer math”, showing the number ring: http://www.cs.nmsu.edu/~pfeiffer/hc11/notes/neg.html

• Notes on Binary Numbers, Arithmetic, and Radix Conversions: http://www.cs.nmsu.edu/~pfeiffer/hc11/notes/binary.html

• Converting hex to decimal using bit flipping and adding one: http://www.madsci.org/posts/archives/2000-02/950277263.Cs.r.html

• Base Converter: Convert numbers in any base up to 32: http://www.cut-the-knot.org/binary.shtml

• Hex (only) to decimal and binary converter, and vice-versa:

  • http://www.easycalculation.com/hex-converter.php
  • http://www.easycalculation.com/decimal-converter.php

• Understanding binary: http://www.exploringbinary.com/

• The Four Stages of Floating-Point Competence: http://www.exploringbinary.com/the-four-stages-of-floating-point-competence/

2.4 From the Classroom Whiteboard/ChalkboardIndex

• Your in-class notes go here.

• Midterm Test One Date (Doodle Poll): check your EMail or look for the Announcement on Blackboard.

• Date extension granted for Assignment #03.

• Write 4-bit 1010(2) as hex, unsigned, s/m, one’s, two’s, and bias-8

  • Answer: A 10 -2 -5 -6 +2
  • now try 1100(2)

• 11 bits holds 2^11 numbers (2^11 = 2^1 * 2^10 = 2 * 1024 = 2048 numbers)

  • if all positive (unsigned): 0 to 2047
  • if two’s complement, half are negative, so -1024…-1,0,+1…+1023

• Integers have no gaps. If range is -1024 to +1023, no integers are missing.

• Multi-byte integers and endian-ness 080_byte_order_endian.html and 05.ppt #7

Author: 
| Ian! D. Allen  -  idallen@idallen.ca  -  Ottawa, Ontario, Canada
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