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
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-
Equation 6.7 Fractional format
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.
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