Texas Instruments MSP430x4xx Family, User Manual

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32-Bit Hardware Multiplier Operation
9-10 32-Bit Hardware Multiplier
9.2.4 Fractional Numbers
The 32-bit multiplier provides support for fixed-point signal processing. In
fixed−point signal processing, fractional number are represented by using a
fixed decimal point. To classify different ranges of decimal numbers, a
Q-format is used. Different Q-formats represent different locations of the
decimal point. Figure 9−2 shows the format of a signed Q15 number using 16
bits. Every bit after the decimal point has a resolution of 1/2, the most
significant bit is used as the sign bit. The most negative number is 08000h and
the maximum positive number is 07FFFh. This gives a range from −1.0 to
0.999969482
≅
1.0 for the signed Q15 format with 16 bits.
Figure 9−2. Q15 Format Representation
S
1
2 1
4 1
8 1
16
...
Decimal number equivalent
Decimal point
Sign bit
15 bits
The range can be increased by shifting the decimal point to the right as shown
in Figure 9−3. The signed Q14 format with 16 bits gives a range from −2.0 to
1.999938965
≅
2.0.
Figure 9−3. Q14 Format Representation
S
1
2 1
4 1
8 1
16
... x
14 bits
The benefit of using 16-bit signed Q15 or 32-bit signed Q31 numbers with
multiplication is that the product of two number in the range from −1.0 to 1.0
is always in that same range.