C.1 Overview - Analog Devices ADSP-2106x SHARC User Manual

C.1 OVERVIEW
The ADSP-2106x supports the 32-bit single-precision floating-point data
format defined in the IEEE Standard 754/854. In addition, the ADSP-
2106x supports an extended-precision version of the same format with
eight additional bits in the mantissa (40 bits total). The ADSP-2106x also
supports 32-bit fixed-point formats—fractional and integer—which can be
signed (twos-complement) or unsigned.
C.2 IEEE SINGLE-PRECISION FLOATING-POINT DATA FORMAT
IEEE Standard 754/854 specifies a 32-bit single-precision floating-point
format, shown in Figure C.1. A number in this format consists of a sign
bit s, a 24-bit significand, and an 8-bit unsigned-magnitude exponent e.
For normalized numbers, the significand consists of a 23-bit fraction f and
a "hidden" bit of 1 that is implicitly presumed to precede f 22 in the
significand. The binary point is presumed to lie between this hidden bit
and f 22 . The least significant bit (LSB) of the fraction is f 0 ; the LSB of the
exponent is e 0 . The hidden bit effectively increases the precision of the
floating-point significand to 24 bits from the 23 bits actually stored in the
data format. It also insures that the significand of any number in the IEEE
normalized-number format is always greater than or equal to 1 and less
than 2.
The unsigned exponent e can range between 1 ≤ e ≤ 254 for normal
numbers in the single-precision format. This exponent is biased by +127
(254 ÷ 2). To calculate the true unbiased exponent, 127 must be subtracted
from e.
31 30 23
s e • • • e
7 0
Hidden Bit
Figure C.1 IEEE 32-Bit Single-Precision Floating-Point Format
www.BDTIC.com/ADI
Numeric Formats
22
1 . f • • •
22
Binary Point
C
0
f
0
C – 1