1. CSE 575 Computer Arithmetic Spring 2002 Mary Jane Irwin (www. cse. psu
CSE 575 Computer Arithmetic Spring Mary Jane Irwin (
Do seating chart next class

2. An Initial Request
While you are welcome to use, modify, expand on the slides contained in this slide set, I do ask that you acknowledge my (considerable) efforts in some way. One way is to acknowledge that your slides are adapted from mine on the first slide of each set of slides - or to retain my copyright.

3. Course Structure and Goals
The slides are for a 15 week (full semester) second level graduate computer science and engineering course.
The course, CSE 575, covers advanced topics in computer arithmetic based on the text by Parhami, Computer Arithmetic Algorithms and Hardware Designs, Oxford Press, 2000.
The course prerequisites are a senior undergraduate level VLSI design course (based on Rabaey’s text) and a senior undergraduate level computer architecture course (based on Patterson/Hennessy’s text).

4. Course Outline Week Topic Reading HW 1 Overview; number representation
Chp 1 and 2 2
Addition (CLA’s); project discussions
Chp 5,
HW1 3
Fast adders (skip, select, prefix, etc.)
Chp , 7 4
Redundant representation and sign digit adders
Chp 3 5
Multi-operand adders
Chp 8
HW2 6
Multipliers (serial and fast parallel)
Chp 9, 10 7
More on fast multipliers; array multipliers
Chp 10, 11 8
Division (serial and base 2 SRT)
Chp 13, 14
HW3 9
Higher radix dividers; array dividers
Chp 15 10
Convergence dividers; square rooters
Chp 16, 21 11
Floating point representation and arithmetic
Chp 17, 18
HW4 12
CORDIC and CS/P function evaluators
Chp 22, 23 13
Semester exam; table look-up arithmetic
Chp 24 14
Residue and logarithmic repr. and arithmetic
Chp 4, 17.6, 18.6 15
Presentation of student design projects

5. Things to be Aware Of
Throughout the set of slides, you will often see two slides that are almost identical. One is for the class handout and is missing some key points (it is marked in the notes section as “for class handout”). The other is for lecture (marked “for lecture”) where the key points are included and are animated to appear as students respond to questions posed to them in class.
Put the “for lecture” slide in hide mode when preparing class handouts and the “for class handouts” in hide mode when preparing lectures
A sample pair of slides follows

6. 4-Bit CLA A constant time adder!?! Except we have not limited fan-in!
gi = xi yi
pi = xi  yi
si = pi  ci c2 c2 c1 +1 1 s3 s2 s1 s0 g3 p3 g2 p2 g1 p1 g0 p0 c4 +2 c0
c1 = g0 v p0c0
c2 = g1 v p1g0 v p1p0c0
c3 = g2 v p2g1 v p2p1g0 v p2p1p0c
c4 = g3 v p3g2 v p3p2g1 v p3p2p1g0 v p3p2p1p0c0
For lecture
ci+1 requires i+2 inputs to the largest AND or OR term, so only really feasible for n = 4 as shown
May want to form c4 from g3, p3 and c2 in the normal way if speed of c4 is not an issue
Assume can form gi and pi is one delay unit, the c terms in 2 units, and the final sum in one unit, then c1, c2, c3, and c4 are all ready in 3 units and s1, s2, s3 are ready one more unit later (4 units) (s0 is ready in 2 units)
A constant time adder!?!
Except we have not limited fan-in!

7. Notation Used (Mostly)
X - (capital letters) full precision operand consisting of multiple bits (base 2) or digits (base 2 and higher)
X =  xiri = (xk-1 xk-2 … x1 x0. x-1 x-2 … x-l+1 x-l )r
xi - (small letters) single bit or digit values (i negative then a fractional bit/digit, i positive then an integer bit/digit)
Xi - (capital letters) full precision result from the ith iteration of a computation