Computer Arithmetic - Spring 2000

 
Dr. Guy Even

The Computer Arithmetic course is about how to design an Arithmetic Logic Unit (ALU) and a Floating Point Unit. The course deals with the mathematical foundation as well as the hardware implementation.

place & time

Tuesdays 18-20, Room 201, Dan-David Building.

remark: class on first week of the semester (i.e. 22/02/00) will not be held. We will schedule an extra class instead of it.

homework

• Assignment #1 - shift & add multiplier (missing photo-copied pages) (postscript file).
• Assignment #2 - IEEE Rounding: the Decomposition Theorem (postscript file).
• Assignment #3 - FP-ADD, Sticky bit computation in FP-MUL, composing rounding (postscript file).

e-mail distribution list

To join the list, leave the list, read old postings, etc. visit: http://post.tau.ac.il/archives/eng0511-5548-01.html

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Please use this channel for topics related to the course (questions about material from the class or from homework). I will do my best to reply quickly.

syllabus & schedule

1.

Brief review of integer arithmetic:

(a)

fast binary addition (parallel prefix adder) (1 lecture).
Good notes of this lecture were prepared last year (Gzipped postscript file [198KB]).

(b)

signed addition/subtraction (two's complement representation: definition & properties, main theorem: reduction of signed addition to unsigned addition, implementation) (1 lecture) Lecture notes (read with a grain of salt): prepared by Eran Knaz Word File [265KB] and prepared by Moshe Yehonadav Word File [292KB] and prepared by Mark Elnekave (.pdf file, 214KB) .

(c)

multiplication (shift & add, arrays, addition trees, extension to signed numbers) (1 lecture) Lecture notes: Previous notes and Booth Encoding is covered in prepared by Ziv Gilad Word File [265KB]

2.

IEEE floating point standard (2 lectures)

3.

Generic IEEE rounding (1 lecture)

4.

Floating point multiplication (1 lecture)

5.

Floating point addition (2 lectures)

6.

Floating point division (2 lectures)

7.

Recodings, the pipelined packet forwarding paradigm, and floating point adder/multiplier that conform with the paradigm. (2 lectures)

requirements

1.

(25% of final grade) Home work assignments (expect at least 4 assignments).

2.

(25% of final grade) Take-home exam (to be submitted in printed form).

3.

(50% of final grade) Project (VHDL design & simulation, animation of FP algorithms, extending an FP algorithm and testing it, etc.). Excellent projects can serve as a basis for a Master's project and even a thesis.

references

A short list of references appears here. Another option is to read class notes written in the past two years by students taking the course. Some of these class notes are pretty good - however, read with a (big) grain of salt. Class notes: Spring 98 and Spring 99.

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