In this paper we are considering problems of division and multiplication in a computational environment in which all basic arithmetic algorithms satisfy "on-line" property: to generate jth digit of the result it is necessary and sufficient to have argument(s) available up to the (j+δ)th digit, where the index difference 6 is a small positive constant. Such an environment, due to its potential to perform a sequence of operations in an overlapped fashion, could conveniently speed up an arithmetic multiprocessor structure or it could be useful in certain real-time applications, with inherent on-line properties. The on-line property implies a left-to-right digit-by-digit type of algorithm and consequently, a redundant representation, at least, of the results. For addition and subtraction such algorithms, satisfying on-line property, can be easily specified. Multiplication requires a somewhat more elaborate approach and there are several possible ways of defining an on-line algorithm. However, the existence of an on-line division algorithm is not obvious and its analysis appears interesting.
[1]
Edward L. Braun.
Digital computer design - logic, circuitry, and synthesis
,
1963
.
[2]
Daniel Ewell Atkins,et al.
A study of methods for selection of quotient digits during digital division
,
1970
.
[3]
A. Avizeinis,et al.
Signed Digit Number Representations for Fast Parallel Arithmetic
,
1961
.
[4]
Milos D. Ercegovac.
A general method for evaluation of functions and computations in a digital computing
,
1975,
1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH).
[5]
James E. Robertson,et al.
A New Class of Digital Division Methods
,
1958,
IRE Trans. Electron. Comput..