Java Reference

In-Depth Information

The ciphers representing the number can be found iteratively using the

following equations:

value
i

B
i

B
i
+
1

value
n
=

number
;
c
i
=

;
value
i
=

value
i
+
1
−

c
i
+
1

·

Equation 6.4
Ciphers for representation in base B

Representation format

The most used format is the fixed point format: it is the basic positional

format described above. The other two formats are based on the fixed point

format. According to the floating point format a number is represented as:

B
exponent

number

=

mantissa

·

Equation 6.5
Floating point format

Here
mantissa
is a fixed point number that has a single cipher before the

decimal point,
B
is the base, and
exponent
is an integer number (i.e. a fixed

point with no cipher after the decimal point). The conversion between a

fixed point and a floating point format can be performed using the following

formula, where
c
i

is a cipher of the fixed point format while
f
i

is a cipher of

the mantissa of the floating point number.

B
n
−
1

c
n

...

c
2
c
1
c
0

.

c
−
1
c
−
2

...

c
−
m
=

f
0

.

f
−
1
f
−
2

...

f
−
(
n
+
m
−
1)
+

Equation 6.6
Equivalence between fixed point and floating point

The fractional format is the most common way of representing rational

numbers. A number is represented as the division of numerator and denom-

inator:

numerator

denominator

number

=

Equation 6.7
Fractional format

6.2.2

Main features

We are now able to summarize all the main features emerging from the

problem analysis.

Arithmetic operations
. The calculator should be able to perform binary

arithmetic operations.

■

Multi-format representation
. The calculator should allow the user to

insert operands in different number formats, to switch between formats,

and to convert results from one format to another.

■

Multi-base representation
. Similarly, the calculator should allow the user

to insert operands in different number bases, to switch between bases,

and to convert results from one base to another.

■