2 Lecture Notes for This WeekIndex

2.1 From the Class Notes link on the Course Home PageIndex

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
085_floating_point_tenth.txt - Exploring approximations to “one tenth” in binary floating point
090_FloatingPoint.html - Floating Point Encoding
FunnyMath1.java - another program that produces unexpected incorrect results

2.1.1 AssignmentsIndex

Assignment #04 - Integer Numeric Conversions
- Marks are awarded for original work, not for cut-and-paste. Any answers that are found to be cut-and-paste from some other document will require you to resubmit the entire lab as hand-written (and may result in a charge of plagiarism or academic fraud as well). Do your own thinking; write your own answers.
000_self_mark.txt - Self-mark of Assignment NN (participation mark)

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
06.ppt - Memory
- only read memory speeds 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: In class on Friday, October 14. Short answer and multiple choice.
000_self_mark.txt - Self-mark of Assignment NN (participation mark)
Memory speeds (latencies) (06.ppt #7)
- 1ns-2ns - registers
- 3ns-10ns - Level 1 Cache
- 25ns-50ns - Level 2 Cache
- 30ns-90ns - main memory
- 5ms-20ms - fixed hard disk
- Source: [6.ppt] slide 7 (under [Blackboard] Course Content - Slides)

2.4.1 Floating PointIndex

Review last week. Look at the 1/10 example program.
IEEE754 Single Precision: one bit sign, eight bits exponent, 23+1 bits of significand (mantissa). (The leftmost “1.” bit is assumed.)
Write 1.0 decimal as normalized binary: +1.0 * 2^0
- sign: +
- exponent of 2: 0
- mantissa/significand: 1.0
- as IEEE754 S.P. in binary?
  - 8-bit exponent 0 goes in as excess-127, so 0+127 = 127 = 01111111(2)
  - Answer: 0 01111111 00000000000000000000000(2)
- What is the next IEEE754 S.P number greater than 1.0?
  - Smallest change to significand is from 00000000000000000000000 to 000000000000000000000001 or 2^-23
  - multiply by exponent 2^0: 2^-23 * 2^0 = 2^-23
  - next number is 1.0 + 2^-23
Write 8388608 decimal as normalized binary: +1.0 * 2^23
- sign: +
- exponent of 2: 23
- mantissa/significand: 1.0
- As IEEE754 S.P. in binary?
  - 8-bit exponent 23 goes in as excess-127, so 23+127 = 150 = 10010110(2)
  - Answer: 0 10010110 00000000000000000000000(2)
- What is the next IEEE754 S.P number greater than 8388608?
  - Smallest change to significand is from 00000000000000000000000 to 000000000000000000000001 or 2^-23
  - multiply by exponent 2^23: 2^-23 * 2^23 = 2^0 = 1
  - next number is 8388608 + 1 = 8388609
See the 02.ppt slide set, but don’t read all the slides.
Coming up next: Character data

Author: 
| Ian! D. Allen  -  idallen@idallen.ca  -  Ottawa, Ontario, Canada
| Home Page: http://idallen.com/   Contact Improv: http://contactimprov.ca/
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Week 05 Notes for CST8281 - Fall 2011

1 Midterm Test #1 - 15%Index

2 Lecture Notes for This WeekIndex

2.1 From the Class Notes link on the Course Home PageIndex

2.1.1 AssignmentsIndex

2.2 From Blackboard Course DocumentsIndex

2.3 From the InternetIndex

2.4 From the Classroom Whiteboard/ChalkboardIndex

2.4.1 Floating PointIndex