On June 19, 2007, Professor Parhami's UCSB ECE website moved to a new location. For an up-to-date version of this page, visit it at the new address: http://www.ece.ucsb.edu/~parhami/res_comp_arith.htm
the following descriptions, selected items from B.
Parhami’s list of publications are provided in brackets.
Arithmetic is a branch of
mathematics that deals with numbers and numerical computation. Arithmetic
operations on pairs of numbers x and y include addition (producing
the sum s = x + y), subtraction (yielding the difference d
= x – y), multiplication (resulting in the product p = x
y), and division (generating the quotient q = x / y).
Subtraction and division can be viewed as operations that undo the effects of
addition and multiplication, respectively. Computer arithmetic is a branch of
computer engineering that deals with methods of representing integers
(fixed-point numbers) and real values (e.g., floating-point numbers) in digital
systems and efficient algorithms for manipulating such numbers by means of
hardware circuits or software routines [EncyIS]. On the hardware side, various
types of adders, subtractors, multipliers, dividers, square-rooters, and circuit
techniques for function evaluation are considered . Both abstract
structures and technology-specific designs are dealt with. Software aspects of
computer arithmetic include complexity, error characteristics, stability, and
certifiability of computational algorithms.
in many computer applications is critically dependent on the speed of arithmetic
operations. The discovery, in the mid 1990s, of design flaws in the arithmetic
circuits of Intel’s Pentium processor aptly demonstrated the need for a more
systematic approach to the design and verification of arithmetic algorithms and
associated hardware designs, especially when they are extensively optimized for
speed. Criteria other than speed are also becoming important in the design of
algorithms and hardware for computer arithmetic. Examples include accuracy, high
throughput, fault tolerance, certifiability, and low power consumption. Dr.
Parhami’s research deals with all of the aspects above. Because at very high
clock rates, carry propagation (even with the fastest carry networks) becomes a
limiting factor for speed, a key area of Professor Parhami’s research deals with
redundant number representations and the associated carry-free arithmetic