TAS5711
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SLOS600 –DECEMBER 2009
The decimal value of a 3.23 format number can be found by following the weighting shown in Figure 54. If the
most significant bit is logic 0, the number is a positive number, and the weighting shown yields the correct
number. If the most significant bit is a logic 1, then the number is a negative number. In this case every bit must
be inverted, a 1 added to the result, and then the weighting shown in Figure 55 applied to obtain the magnitude
of the negative number.
21 Bit
20 Bit
2–1 Bit
2–4 Bit
2–23 Bit
(1 or 0) ´ 21 + (1 or 0) ´ 20 + (1 or 0) ´ 2–1 + ....... (1 or 0) ´ 2–4 + ....... (1 or 0) ´ 2–23
M0126-01
Figure 55. Conversion Weighting Factors—3.23 Format to Floating Point
Gain coefficients, entered via the I2C bus, must be entered as 32-bit binary numbers. The format of the 32-bit
number (4-byte or 8-digit hexadecimal number) is shown in Figure 56
Fraction
Digit 6
Sign
Bit
Fraction
Digit 1
Fraction
Digit 2
Fraction
Digit 3
Fraction
Digit 4
Fraction
Digit 5
Integer
Digit 1
u
u
u
u
u
u
x
x.
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x x x x
0
S
Coefficient
Digit 8
Coefficient
Digit 7
Coefficient
Digit 6
Coefficient
Digit 5
Coefficient
Digit 4
Coefficient
Digit 3
Coefficient
Digit 2
Coefficient
Digit 1
u = unused or don’t care bits
Digit = hexadecimal digit
M0127-01
Figure 56. Alignment of 3.23 Coefficient in 32-Bit I2C Word
Table 2. Sample Calculation for 3.23 Format
dB
0
Linear
1
Decimal
8,388,608
14,917,288
4,717,260
Hex (3.23 Format)
0080 0000
5
1.7782794
0.5623413
L = 10(X/20)
00E3 9EA8
–5
X
0047 FACC
D = 8,388,608 × L H = dec2hex (D, 8)
Table 3. Sample Calculation for 9.17 Format
dB
0
Linear
1
Decimal
131,072
Hex (9.17 Format)
2 0000
5
1.77
231,997
3 8A3D
–5
X
0.56
L = 10(X/20)
73,400
1 1EB8
D = 131,072 × L
H = dec2hex (D, 8)
Copyright © 2009, Texas Instruments Incorporated
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