TAS3103ADBT datasheet(64/154 Pages) TI2

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3−1

3 Firmware Architecture

3.1

I2C Coefficient Number Formats

The firmware for the TAS3103A is housed in ROM resources within the TAS3103A and cannot be altered. However,

mixer gain, level offset, and filter tap coefficients, which can be entered via the I2C bus interface, provide a user with

the flexibility to set the TAS3103A to a configuration that achieves the system-level goals.

The firmware is executed in a 48-bit signed fixed-point arithmetic machine. The most-significant bit of the 48-bit data

path is a sign bit, and the 47 lower bits are data bits. Mixer gain operations are implemented by multiplying a 48-bit

signed data value by a 28-bit signed gain coefficient. The 76-bit signed output product is then truncated to a signed

48-bit number. Level offset operations are implemented by adding a 48-bit signed offset coefficient to a 48-bit signed

data value. In most cases, if the addition results in overflowing the 48-bit signed number format, saturation logic is

used. This means that if the summation results in a positive number that is greater than 0x7FFF FFFF FFFF (the

spaces are used to ease the reading of the hexadecimal number), the number is set to 0x7FFF FFFF FFFF. If the

summation results in a negative number that is less than 0x8000 0000 0000, the number is set to 0x8000 0000 0000.

There are exceptions to the use of saturation logic for summations that overflow—see Digital Audio Processor (DAP)

Arithmetic Unit, Section 2.4.

3.1.1

28-Bit 5.23 Number Format

All mixer gain coefficients are 28-bit coefficients using a 5.23 number format. Numbers formatted as 5.23 numbers

means that there are 5 bits to the left of the decimal point and 23 bits to the right of the decimal point. This is shown

in the Figure 3−1.

2−23 Bit

S_xxxx.xxxx_xxxx_xxxx_xxxx_xxxx_xxx

2−4 Bit

2−1 Bit

20 Bit

Sign Bit

23 Bit

Figure 3−1. 5.23 Format

The decimal value of a 5.23-format number can be found by following the weighting shown in Figure 3−2. 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 3−2 applied to obtain the magnitude of the negative

number.

(1 or 0)

y 23 + (1 or 0) y 22 + … + (1 or 0) y 20 + (1 or 0) y 2−1 + … + (1 or 0) y 2−4 + … + (1 or 0) y 2−23

23 Bit

22 Bit

20 Bit

2−1 Bit

2−4 Bit

2−23 Bit

Figure 3−2. Conversion Weighting Factors—5.23 Format to Floating Point

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