4-4
ColdFire CF4e Core User’s Manual
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Operand Data Formats and Types
Figure 4-2. Mantissa
The integer bit is implied to be set for normalized numbers and infinities, clear for zeros
and denormalized numbers. For not-a-numbers (NANs), the integer bit is ignored. The
exponent in both floating-point formats is an unsigned binary integer with an implied bias
added to it. Subtracting the bias from exponent yields a signed, two’s complement power
of two. This represents the magnitude of a normalized floating-point number when
multiplied by the mantissa.
By definition, a normalized mantissa always takes values starting from 1.0 and going up
to, but not including, 2.0; that is, [1.0...2.0).
4.2.3 Floating-Point Data Types
Each floating-point data format supports five unique data types: normalized numbers,
zeros, infinities, NANs, and denormalized numbers. The normalized data type, Figure 4-3,
never uses the maximum or minimum exponent value for a given format.
4.2.3.1 Normalized Numbers
Normalized numbers include all positive or negative numbers with exponents between the
maximum and minimum values. For single- and double-precision normalized numbers,
the implied integer bit is one and the exponent can be zero.
Figure 4-3. Normalized Number Format
4.2.3.2 Zeros
Zeros can be positive or negative and represent real values, + 0.0 and – 0.0. See
Figure 4-4.
Figure 4-4. Zero Format
(integer bit).(fraction)
Mantissa
Min
<
Exponent
<
Max
Fraction = Any bit pattern
Sign of Mantissa, 0 or 1
Exponent = 0
Fraction = 0
Sign of Mantissa, 0 or 1
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.