Digital Arithmetic

248 r H A pTER 5 Division by Digit Recurrence

5ot

Definition and Notation

The division operation is defined by the following expressions:

x - q .d +rein

5.1

and

[rein]

< Id["

ulp

and

sign(rein) = sign(x) 5.2

where the

dividend x

and the

divisor d

are the operands and the results are the

quotient q

and, optionally, the

remainder rem.

The unit in the last position

(ulp)

defines the granularity of the quotient. The two most typical cases produce a

fractional quotient or an integer quotient. For these cases we have

9 fractional quotient:

ulp = r-n

(for radix-r representation and n-digit

quotient)

9 integer quotient:

ulp ...