The coefficients of the recording path mixers [like a_x, b_x, c_x, d_x] are programmed as 32-bit twos-complement values, each occupying four consecutive registers in the register space of the device. These mixer coefficients are in either 1.31 format with a range from –1 (0x80000000) to 0.9999999995 (0x7FFFFFFF), or 2.30 format with a range from – 2(0x80000000) to 1.9999999991 (0x7FFFFFFF). These representations are shown in Figure 2-2.

• To convert a floating point number to the corresponding Q31 format, multiply the floating point mixer coefficient by 2³¹ (for 1.31) or 2³⁰ (for 2.30) and truncate to the nearest integer.
  • For example, a coefficient of 0.4 corresponds to an integer value of 858993459 in 1.31 format.
  • Similarly, a coefficient of 1.25 corresponds to an integer value of 1288490189 in 2.30 format

• For positive integers, convert directly to hexadecimal format.
• For negative integers, take the absolute value of the coefficient, convert the value to binary, negate the value, add one, and convert to hex. For example, to represent -135 in 32-bit two's complement hexadecimal format:
  • Absolute value of -135 is 0000 0000 0000 0000 0000 0000 1000 0111 in binary (or 0x00000087 in hex)
  • Negating the binary results in 1111 1111 1111 1111 1111 1111 0111 1000 in binary (or 0xFFFFFF78 in hex). This is the twos-complement representation of the negative integer.